'Could there not be a similar disconnect when you try to take GR beyond just looking at solar systems, stars, and galaxies, and to the level of clusters, superclusters, and the universe at large?'
Yes, absolutely. But alternatives to GR are highly constrained by tests in the solar system and in binary pulsars. Even if you go out to superclusters and very high redshift the functional form of the theory is tight by big bang nucleosynthesis.
For instance you can add a term that goes something like R (scale factor) in the field equations, but not R^2 or 1/R or even log R. And again, you can perturb such a theory around a FRW manifold, and out pops the old cosmological constant as a first order approximation. Which means the language we are speaking in, is at least right.
Theres not much phase space to work in, and Occams razor tends to favor the simpler theory.
Now, one of the three solutions to the standard cosmology taught to me long before we knew what we were dealing with, was in fact the very one we see now.. With a cosmological constant (or if you like to interpret it differently, a steady state equation that admits negative pressure). GR was silent on which of the three simplest solutions we lived in, it was only when data came in on a few undetermined variables, did it exactly fix the rest of the theory into implying a Desitter vacuum, and later independantly verified by other means. Moreover, it doesn't solve another huge problem that the cosmological constant poses.. Namely, the coincidence problem.
The point is, theres nothing really inconsistent with GR by measurement, only very strange, perhaps coincidental puzzles.
Not so with quantum field theory. Its quantum mechanics that seems to fail observation at this time, since the theory predicts a number so incredibly off. Many great theorists have worked on the problem however, and it seems that yes indeed we might have to alter the functional form of general relativity at very small scales, in order to have any hope of reconciling the two. One then gets rid of naive topological notions like manifolds for instance, and replaces it with a more invariant formalism (for instance projective diffeomorphism group constructs, or spaces of connections on some underlying guage field).
You should realize however, the most straight forward and simple field theory of a spin 2 hypothetical Graviton mediator, that tries to work in curved space independantly outputs Einsteins eqns (well actually its off by a puzzling constant factor of about 1.2 in the weak field limit, but whatever).
So this stuff isn't just working in a vacuum, theres a lot of independant theory that agrees with GR and rederives it and the assumptions that go into GR are about the most lenient one can make (isotropy, homogeneity, rotational invariance, locally reducable to special relativity)... blah blah blah.
Personally, I accept GR and the geometry that it now implies globally, in fact probably more accurate as you get to large scale rather than viceversa. But ultimately I do think its just a statistical limit (much like current quantum mechanics) of a more profound black box called quantum gravity, that occurs at extreme energies around the Planck scale.
