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One of my hangups with evolution is that neither Darwin, Gould, nor I, believe that it is supported by fossil evidence.

This is very incorrect.

Let's see what Gould *ACTUALLY* says on this subject, shall we?

"We believe that Huxley was right in his warning. The modern theory of evolution does not require gradual change. In fact, the operation of Darwinian processes should yield exactly what we see in the fossil record."
- Gould, Stephen J. The Panda's Thumb, 1980, p. 181-182
"It [PE] represents no departure from Darwinian mechanisms."
-- Gould and Eldredge 1977, Section IV, "PE as the basis for a Theory of Macroevolution", page 139
"Evolution is a theory of organic change, but it does not imply, as many people assume, that ceaseless flux is the irreducible state of nature and that structure is but a temporary incarnation of the moment. Change is more often a rapid transition between stable states than a continuous transformation at slow and steady rates."
-- Gould, Stephen Jay 1980. "A Quahog is a Quahog", The Panda's Thumb. New York: W.W. Norton & Co., pp. 204-13
"Many colleagues thought that we had raised the old anti-Darwinian specter of macromutationism, or truly sudden speciation in a single generation by a large and incredibly lucky mutation. I do not know why this happened; I think that all our articles and public statements were clear in separating human from geological rapidity. The theory, after all, is rooted in this distinction —- for punctuated equilibrium is the recognition that gradualism on our mortal measuring rod of three score years and ten translates to suddenness at the planet's temporal scale."
-- S. J. Gould, "Opus 200"
"For a variety of reasons, small isolated populations have unusual potential for effective change: for example, favorable genes can quickly spread throughout the population, while the interaction of random change (rarely important in large populations) with natural selection provides another effective pathway for substantial evolution. Even with these possibilities for accelerated change, the formation of a new species from a peripherally isolated population would be glacially slow by the usual standard of our lifetimes. Suppose the process took five to ten thousand years. We might stand in the midst of this peripheral isolate for all our earthly days and see nothing in the way of major change. But now we come to the nub of punctuated equilibrium. Five to ten thousand years may be an eternity in human time, but such an interval represents an earthly instant in almost any geological situation—a single bedding plane (not a gradual sequence through meters of strata)."
-- Ibid.
"What then is the expected geological expression of speciation in a peripherally isolated population? The answer is, and must be, punctuated equilibrium. The speciation event occurs in a geological instant and in a region of limited extent at some distance from the parental population. In other words, punctuated equilibrium—and not gradualism—is the expected geological translation for the standard account of speciation in evolutionary theory. Species arise in a geological moment—the punctuation (slow by our standards, abrupt by the planet's). [...] Most of our paleontological colleagues missed this insight because they had not studied evolutionary theory and either did not know about allopatric speciation or had not considered its translation to geological time. Our evolutionary colleagues also failed to grasp the implication, primarily because they did not think at geological scales."
-- Ibid.
"Charles Darwin often remarked that his revolutionary work had two distinct aims: first, to demonstrate the fact of evolution (the genealogical connection of all organisms and a history of life regulated by "descent with modification"); second, to advance the theory of natural selection as the most important mechanism of evolution. Darwin triumphed in his first aim (American creationism of the Christian far right notwithstanding). Virtually all thinking people accept the factuality of evolution, and no conclusion in science enjoys better documentation. Darwin also succeeded substantially in his second aim. Natural selection, an immensely powerful idea with radical philosophical implications, is surely a major cause of evolution, as validated in theory and demonstrated by countless experiments.
S. J. Gould, "The New York Review of Books", Volume 44, Number 10 · June 12, 1997
"...may I state for the record that I (along with all other Darwinian pluralists) do not deny either the existence and central importance of adaptation, or the production of adaptation by natural selection. Yes, eyes are for seeing and feet are for moving. And, yes again, I know of no scientific mechanism other than natural selection with the proven power to build structures of such eminently workable design."
-- Ibid.

Or as accurately summarized by another author:

"But Gould, Eldredge and Stanley are talking about the failure of the fossil record to document fine-scale transitions between pairs of species, and its dramatic documentation of rapid evolutionary bursts involving multiple speciation events -- so-called adaptive radiations. They are not talking about any failure of the fossil record to document the existence of intermediate forms (to the contrary, there are so many intermediates for many well-preserved taxa that it is notoriously difficult to identify true ancestors even when the fossil record is very complete). Nor are Gould, Eldredge, and Stanley talking about any failure of the fossil record to document large-scale trends, which do exist, however jerky they may be. Furthermore, fine-scale transitions are not absent from the fossil record but are merely underrepresented. Eldredge, Gould. and Stanley reason that this is the unsurprising consequence of known mechanisms of speciation. Additionally, certain ecological conditions may favor speciation and rapid evolution, so new taxa may appear abruptly in the fossil record in association with adaptive radiation. Since creationists acknowledge that fine-scale transitions (including those resulting in reproductive isolation) exist and since the fossil record clearly documents large-scale "transitions," it would seem that the creationists have no case. Indeed. they do not. Their case is an artifact of misrepresentation to the lay public of exactly what the fossil record fails to document."
-- Laurie R. Godfrey, "Scientific Creationism: The Art of Distortion", 1984

And for anyone who thinks that Gould's "Punctuated Equilibrium" is somehow a departure from Darwin's own view:

I further believe that these slow, intermittent results accord well with what geology tells us of the rate and manner at which the inhabitants of the world have changed." (Darwin, Ch. 4, "Natural Selection," pp. 140-141)
But I must here remark that I do not suppose that the process ever goes on so regularly as is represented in the diagram, though in itself made somewhat irregular, nor that it goes on continuously; it is far more probable that each form remains for long periods unaltered, and then again undergoes modification. (Darwin, Ch. 4, "Natural Selection," pp. 152)
"It is a more important consideration ... that the period during which each species underwent modification, though long as measured by years, was probably short in comparison with that during which it remained without undergoing any change." (Darwin, Ch. 10, "On the imperfection of the geological record," p. 428)
"Widely ranging species vary most, and varieties are often at first local, -- both causes rendering the discovery of intermediate links less likely. Local varieties will not spread into other and distant regions until they are considerably modified and improved; and when they do spread, if discovered in a geological formation, they will appear as if suddenly created there, and will be simply classed as new species. [Charles Darwin, Origin of Species 1st Edition 1859, p.439]

But we continually over-rate the perfection of the geological record, and falsely infer, because certain genera or families have not been found beneath a certain stage, that they did not exist before that stage. We continually forget how large the world is, compared with the area over which our geological formations have been carefully examined; we forget that groups of species may elsewhere have long existed and have slowly multiplied before they invaded the ancient archipelagoes of Europe and of the United States. We do not make due allowance for the enormous intervals of time, which have probably elapsed between our consecutive formations, -- longer perhaps in some cases than the time required for the accumulation of each formation. These intervals will have given time for the multiplication of species from some one or some few parent-forms; and in the succeeding formation such species will appear as If suddenly created.
I may here recall a remark formerly made, namely that it might require a long succession of ages to adapt an organism to some new and peculiar line of life, for instance to fly through the air; but that when this had been effected, and a few species had thus acquired a great advantage over other organisms, a comparatively short time would be necessary to produce many divergent forms, which would be able to spread rapidly and widely throughout the world.
I will now give a few examples to illustrate these remarks; and to show how liable we are to error in supposing that whole groups of species have suddenly been produced.
[many excellent examples snipped for length -- Darwin lists several examples from even his own day of fossils which were thought to have first appeared "suddenly" in certain formations with "no" prior appearance of fossils, only later to discover precursors in earlier formations]
Some few families of fish now have a confined range; the teleostean fish might formerly have had a similarly confined range, and after having been largely developed in some one sea, might have spread widely. Nor have we any right to suppose that the seas of the world have always been so freely open from south to north as they are at present. Even at this day, if the Malay Archipelago were converted into land, the tropical parts of the Indian Ocean would form a large and perfectly enclosed basin, in which any great group of marine animals might be multiplied; and here they would remain confined, until some of the species became adapted to a cooler climate, and were enabled to double the southern capes of Africa or Australia, and thus reach other and distant seas.
-- Charles Darwin, "On the Origin of Species", 1859
Species of different genera and classes have not changed at the same rate, or in the same degree. In the oldest tertiary beds a few living shells may still be found in the midst of a multitude of extinct forms. Falconer has given a striking instance of a similar fact, in an existing crocodile associated with many strange and lost mammals and reptiles in the sub-Himalayan deposits. The Silurian Lingula differs but little from the living species of this genus; whereas most of the other Silurian Molluscs and all the Crustaceans have changed greatly. The productions of the land seem to change at a quicker rate than those of the sea, of which a striking instance has lately been observed in Switzerland. There is some reason to believe that organisms, considered high in the scale of nature, change more quickly than those that are low: though there are exceptions to this rule. The amount of organic change, as Pictet has remarked, does not strictly correspond with the succession of our geological formations; so that between each two consecutive formations, the forms of life have seldom changed in exactly the same degree. Yet if we compare any but the most closely related formations, all the species will be found to have undergone some change. When a species has once disappeared from the face of the earth, we have reason to believe that the same identical form never reappears. The strongest apparent exception to this latter rule, is that of the so- called `colonies' of M. Barrande, which intrude for a period in the midst of an older formation, and then allow the pre- existing fauna to reappear; but Lyell's explanation, namely, that it is a case of temporary migration from a distinct geographical province, seems to me satisfactory.
These several facts accord well with my theory. I believe in no fixed law of development, causing all the inhabitants of a country to change abruptly, or simultaneously, or to an equal degree. The process of modification must be extremely slow. The variability of each species is quite independent of that of all others. Whether such variability be taken advantage of by natural selection, and whether the variations be accumulated to a greater or lesser amount, thus causing a greater or lesser amount of modification in the varying species, depends on many complex contingencies, -- on the variability being of a beneficial nature, on the power of intercrossing, on the rate of breeding, on the slowly changing physical conditions of the country, and more especially on the nature of the other inhabitants with which the varying species comes into competition. Hence it is by no means surprising that one species should retain the same identical form much longer than others; or, if changing, that it should change less. We see the same fact in geographical distribution; for instance, in the land-shells and coleopterous insects of Madeira having come to differ considerably from their nearest allies on the continent of Europe, whereas the marine shells and birds have remained unaltered. We can perhaps understand the apparently quicker rate of change in terrestrial and in more highly organised productions compared with marine and lower productions, by the more complex relations of the higher beings to their organic and inorganic conditions of life, as explained in a former chapter.
-- Charles Darwin, "On the Origin of Species"

This is classic Puncuated Equilibrium -- from Darwin himself.