How much of General relativity follows from the invariance of $c$ and an escape velocity? Just supposing Einstein hadn't come up with his idea of the equivalence principle, leaving him blind for a while. Would he still have been able to come up with General Relativity just using the invariance of the speed of $c$ and gravitational mass having an escape velocity for inertial mass?
In particular, the idea of a black hole dates back to Laplace, which would require the idea of light having to change direction at constant speed to prevent it escaping. There may then be other arguments to show that the bending of light has to take a certain form for smaller gravitational masses.
 A: Escape velocity is unnecessary, and a red herring anyway.
You seem to be equating general relativity with black holes, but the latter are just a small part of the former. Moreover, the fact that the "escape velocity" from a mass $M$ equals $c$ at the Schwarzschild radius $2GM/c^2$ is an unfortunate coincidence. An event horizon has nothing to do with escape velocity. In particular, event horizons allow nothing past them for any amount of time, whereas you can jump off the ground with less than Earth's escape velocity and as a result spend some time off the surface. Newtonian black holes would be visible; the light would go a certain distance and eventually turn around and return to the object.
Arguably GR is just a natural extension of SR, and doesn't need much else for motivation.
This is much more speculative, as all such counterfactuals are. But GR is really built by fully embracing two principles:


*

*The laws of physics, including the constancy of the speed of light, are invariant under coordinate transformations.

*The laws of physics and their invariance are only local. They apply to points, and by continuity to neighborhoods of points to arbitrarily good precision, but they need not apply in some global sense.


The first point is what led to SR in the first place. The second prevents us from limiting ourselves to nice Minkowski space. In hindsight, the second point indicates we should be looking at modeling spacetime with a manifold, which is just a topological object that locally looks flat. And really all GR is is the study of manifolds with certain properties, the most important being that they are locally Minkowski.
Once you're thinking about manifolds, you naturally are lead to equate geodesics with freely moving trajectories. If you make the bold leap to say these should be free-falling trajectories (no non-gravitational forces) rather than Newtonian inertial trajectories (no forces at all, including gravity), then you see that the curvature of the manifold induces gravitational acceleration. You are thus led to search for a relation between this curvature and gravitational mass -- the Einstein equation.
Again this is all in hindsight. There's no way to know for sure what would or would not have been figured out under other circumstances, which is why I'm interpreting the question as "What axioms does one need to get at GR?" My claim is that invariance of $c$, together with the implicit understanding that we are only ever allowed local laws in physics, gets us most of the way there... at least if we know the answer from the outset.
By the way, there are at least three different equivalence principles (sometimes called "weak," "strong," and "Einstein"), and I've never heard any two experts agree on the wording for any of them. I'm sure someone has a formulation of the equivalence principle in which my two points above are in fact just what it says.
