It's true relativity was problematic for Kant's project (particularly re: his thought about Euclidean geometry), and you're right to point to this as an example of science informing philosophical thought.
My understanding is that post-relativity, Neokantians have been trying to reconcile Kant's thought with the implications of relativity. Philosophy as a discipline is, as I understand it, happy to work with new scientific discoveries, and not going to stick with philosophical dogma in the face of contradicting science. Besides, beyond a certain level, doesn't science have to give way to philosophy? I don't see holding certain philosophical assumptions (not really assumptions, but intuitions or propositions argued from intuitions) as a necessarily bad thing or even an avoidable thing, as long as it's open to both philosophical and scientific criticism, where applicable.
At the end of the day I think you're right that Kant's notion of necessary conditions is probably flexible enough to accommodate the findings of general relativity.
The fact that the relation is one of an amendment or a reconciliation to new data is a point in favor of skepticism against his original assumptions, but not a defeater.
I would agree that we can credit intuitions as being more than mere assumptions, and I think you're right about The legitimacy of positing assumptions as long as they're posited in a spirit of openness and responsiveness to philosophical and scientific criticism. What do you know, a healthy and reasonable of reply on philosophy. To tie this to Daniel Dennett, I have found one of his most valuable contributions to be a notion of the principle of charity, which is to credit the person you correspond with with the most reasonable possible interpretation, and I think the best philosophical exchanges are carried out in that spirit, and so I think he would highlight yours as the response in this thread that best embodies that principle.
I'm pretty sure there were already in the 19th century people, like Helmholtz, Riemann etc. who saw themselves as Kantians, but nevertheless developed many of the techniques that later made GR possible (while acknowledging that they challenge Kant's own views) while preserving the core of Kant's theory. See my response above.
My understanding is that post-relativity, Neokantians have been trying to reconcile Kant's thought with the implications of relativity. Philosophy as a discipline is, as I understand it, happy to work with new scientific discoveries, and not going to stick with philosophical dogma in the face of contradicting science. Besides, beyond a certain level, doesn't science have to give way to philosophy? I don't see holding certain philosophical assumptions (not really assumptions, but intuitions or propositions argued from intuitions) as a necessarily bad thing or even an avoidable thing, as long as it's open to both philosophical and scientific criticism, where applicable.