I don't think that anyone is trying sweep anything under the rug, primarily because science has indentified dozens if not hundreds of fossils that they believe track the transition from amphibian to reptile, and from reptile to mammal or bird. Some of them are detailed here.
Your transitional forms can just as easily be interpreted as different species sharing common characteristics.
Given the notoriously imprecise and circular nature of geologic and fossil dating, the organization of fossils into ancestral and descendent can be shown to be the construct of human pre-disposition rather than objective observation. It's a classic case of the assumption forcing the conclusion.
However, that is a matter open to honest debate. What is more interesting to me is the apparent lack of living common ancestors. For example, sharks have existed for 600 million years. They should be the common ancestor of many currently living and extinct species. I am not aware of any study attempting to determine the descendancy of sharks or any other living species. The only work I've seen is an attempt to find common ancestry, and even then, I'm not aware of anyone actually pointing to a fossil and saying: This is the common ancestor of X and Y. It's always X and Y share a common ancestor, Z.
It stands to reason that sharks and other organisms that have existed for hundreds of millions of years should have literally thousands if not millions of species that have them as a common ancestor. Where are they?