I get the impression there is not model for why sometimes thousands of base pairs can fuck off with no impact, and sometimes it changes the organism unrecognizably.

No there's many known reasons that can happen. Here's just some of them, but in the end it all comes down to understanding that genes code for proteins, little molecular machines. Sometimes there are multiple copies of genes that code for similar proteins or even the same protein, so losing one or even more doesn't really do anything as there's more where that came from. Sometimes there are genes that used to be important but no longer have a role or were made redundant, and are free to sedit. If a gene codes for a protein called an enzyme, sometimes a change in the active site that binds the chemicals for the reaction it assists might be catastrophic, but a change elsewhere doesn't do much because it's not as necessary to the function of the protein. Sometimes changes even result in the a similar amino acid or the exact same amino acid getting put at thag spot (since the genetic code has some redundancies, a different combo might still end up being the same).

Many genes code for proteins called transcription factors. Transcription factors help control expression of many other genes, some of which might also be transcription factors that in turn affect other genes, etc. This can create huge cascades. For instance there are things called hox genes that are very important for creating a cascade that leads to the formation of different body segments, and differentiating the different body segments. Mutations in these genes can be devastating, in some animals leading to the dissappearance or redundant addition of whole body segments.

There is tons more to learn of course on specifics in terms of evolution, genetics, and molecular biology of course. I don't think it's comparable to gravity though, which we seem to have a fundamental gap and irreconcilable theories.

At least coming from a background of life sciences personally, it seems to me evolution is probably better understood than gravity. I think a better comparison to gravity in the life sciences might be abiogenesis (how pre life conditions give rise to life to begin with). Once life is going, evolution, that we have a ton on. Not that we know nothing about abiogenesis, but that it's a difficult outstanding problem.

The theory does not need to explain why. It needs to explain how, and prove that it's happening. We know how traits change over time to form new species, and we know that this does in fact happen. There's always more to learn about specifics, but it's almost certainly not changing that evolution is happening, and the mechanisms for that are pretty well understood.