Again I'm seeing a pattern in which inferences you don't like are "conjecture." Science does nothing but gather physical evidence and decide what's the best Occam's Razor interpretation of the overall picture. If you reserve the right up front to brand anything as "conjecture" that would otherwise force you to change your mind, you're doing something unrelated to science. (Probably, you're practicing the pursuit known as "religion.")
I'm just going to show you what you get if you Yahoo! on "myoglobin hemoglobin duplication." From the first link thereon, a page on Duplication Mutations,
Is there evidence that this scenario has happened? Yes, it seems to have happened often. Myoglobin, which stores oxygen in muscles, strongly resembles hemoglobin, which carries oxygen in blood. Both are necessary to humans, but invertebrates such as the worm C. elegans only have one kind of globin. So, it is a reasonable hypothesis that our genes for myoglobin and hemoglobin are "descended" from one single ancestral gene, which got duplicated. And, in fact, there are "unnecessary" structural similarities between human myoglobin and human hemoglobin. If the similarities aren't due to common ancestry, then we have found a really really big coincidence.The second link has lots of swarmy detail on (and several examples of) what you call a "conjecture."
The third link starts by addressing your larger point before diving into Molecular Paleontology.
Life's incessant accumulation of information goes against the grain of the Universe. Whereas most natural processes are dissipating energy and destroying order, life is continually creating it (and using up solar energy in the process). However, the spontaneous emergence of complexity, and hence order, is now thought be a property of many natural processes. Such systems operate at the edge of chaos in that they lie, mathematically, between the readily predictable (ocean tides, phases of the Moon, compound interest) and unpredictable chaos (whitewater turbulence, next month's weather, stock market peaks and troughs).326 hits. Look long enough, you can probably find some creationists in there helping you pretend that nothing means anything you don't want.Thus the information content of Earth life has grown steadily over the past four billion years ...