> vastly conceptually wrong
Only for a useless definition of "wrong". Modeling reality well is an end in itself, and to the extent that model predicts well and "factors" reality cleanly into distinct mechanisms, it is conceptually right. This is all "conceptually right" needs to mean. You can not, as I'm sure you'll agree, even hope to explain the "root cause" of motion and time-evolution. at some point you have to base any theory on some postulate or assumption about why things happen at all. But the point of work like Newton's is to get things right above that level, and he was enormously successful at this.
> mostly Newton played mathematical parlour tricks.
Only for a useless definition of "parlour tricks". The hard part of new ideas (1) is getting to the point where you're posing the right problem and thinking about it the right way. Once you get that right, the predictions (2) hopefully fall out as simple tricks! Then they have to be validated (3) against data—also hard. Newton pulled off all three, the hard parts and the tricks. Not single-handedly, mind you, but almost.
To bring such a big picture into view and fill out its details with credibility was a monumental task. I think of it as akin to evolution developing a new organ system—the genome usually has to find its way down on a very long limb to get there and to be stable enough to stay there. For a species this can happen over many generations, but for a human thinker it is has to happen by imagining and testing many subsequent ideas. Newton did an enormous amount of this on his own, over decades.
> are often incommensurable
Newton being absorbed into relativity is like the one case where they are commensurable. Newton is a clear limiting case! The "ways of thinking" about reality are perhaps not, but nobody (except cranks) is still stuck on Newtonianism at this point.
> as some extension or modification
Obviously it contains new math and new abstractions, as needed to match empirical reality on new data. Its content doesn't extent logically out of Newton, because how could it? The data wasn't there. But the conceptual gesture of devising a mathematical framework which can handle the data is the same one Newton used.
Postscript: philosophy of science folks always like to show up in physics discourse ready to fight various tired, old battles which mostly mattered in the context of the particular ideological dispute of some decade or another. The matter in question is always how to generalize the success of physics by fitting various philsci "models" to the "data" of physics' history. This can be interesting, but they never contribute much to the physics itself, which has always proceeded by its own internally-coherent and immensely-successful logic.