FlyingLemons wrote:
The "dark matter problem" is not a consensus, even in theoretical physics.

It is according to proponents of dark matter theory. But if you're right that reports of a consensus are exaggerated, then I stand properly corrected.
Crazy Eddie wrote:
If I ever did get around to I'd start from the latter  getting the transformations work in a high curvature  and then work backwards to the observational evidence to see if the numbers are (or could be made) consistent with it.

In order to do that, you'd have to first to start reinventing what we know about differential geometry in order to get it to work before even starting to think about applications to physics.

I don't think so, actually. My sense is that this would involve one of those horrendously complicated recursive processes like third or fourth derivative calculus (which I fucking HATE doing, by the way). You wouldn't need to treat a curved space as if it was flat, you'd just need a mathematically consistent way to account for that curvature itself. Which is, like, stupefyingly difficult, but hardly impossible.
As an extreme oversimplification: you have a formula to calculate the surface area of a sphere (general relativity) and to calculate the surface area of a cube (special relativity). The basic problem is that there's no elegant way to calculate the surface area of an irregularly shaped object like, say, a rock or an oddlyshaped peanut. Locallyflat spacetime is a mathematical conceit that doesn't actually exist in reality and so special relativity itself is just an approximation (like using the ideal gas model to calculate drag coefficients on a spacecraft; you can get away with it under some circumstances, but not all).
I'm not, IOW, saying it would be simple or formulaic as such. Really, I'm saying that Einstein's relativity is a paradigm that obfuscates the fact that Minkowski spacetime IS applicable to curved (or rather BUMPY) spacetime and we simply lack an efficient way to calculate those spacetimes much the way we lack an efficient way to calculate the surface area of a oddlyshaped peanut.