From quantum mechanics we know how to describe, statistically, an unbound particle floating in space. Treat it as a dispersing, normalizable, Gaussian wave packet. We know how the wave packet evolves, and can give "what would we measure" descriptions of it's properties by sandwiching the right operator representing some/any physical quantity.
Question 1: why can't we just work with the expectation values of properties of a massive spread-out wave function ( < x >, < p > ), write up some statistical, or averaged version of a stress-energy-momentum tensor, plug it into the Einstein field equations, tidy out issues, and voila: wave-function sourced probabilistic description of the spacetime metric? I'm certain there's some problems with this "program", but what?
Question 2: put two apples into space with a zero relative velocity. Due to gravity, they will eventually move towards each other. Now lets say it's not two apples, but two Gaussian wave packets of neutral particles. What has to be plugged into this two-particle $\Psi$ that would evolve it in a way where the two maxima of the probability density would move closer to each other over time at the right rate?
Especially Q2 seems to be such a simple setup that smart people must have written something up that works, at least approximately.