et me start with the physics, then work back to the history. No, we have nothing to say about gravity without fields or spacetime, a sort of field itself. All of physics, not just gravity, ultimately faces the question of being "unexplained", since at best what we are aiming to do is get a self-consistent, complete and accurate set of laws.* Even if we got that, it would be in some sense just a bunch of unexplained math.
The black-hole stuff is a bit over my head. We don't say that physics breaks down at the singularity, just the physics that we know to this point. From the outside perspective, not even that happens. We think that the in-falling stuff forms a thin sheet just outside the would-be horizon and ultimately evaporates by Hawking-like radiation. A universe that was empty except for a star could have a perfectly ordinary spacetime, which would soon have lots of photons whizzing through it.
On fields- sure they started as a mathematical convenience. At this point, they're all we've got. Physics has no ingredients other than fields.
Your description of the development of relativity sounds fishy. The basic math of Special Relativity was so simple even Einstein could handle it. The 4-D version was due to Minkowski, not to either of the Einsteins. The General Relativistic math was harder. I've heard that the first successful formulation was due to Hilbert, who may have been just barely ahead of Einstein.
*For the in-crowd, no, that needn't violate Gödel's theroem, since not all formal statements need to map to ones with physical significance.
(published on 07/06/2011)