What would superposition look like in Wheeler-deWitt? Each Hilbert space vector would represent a single spacetime manifold, metric and stress-energy tensor with no "meta" time dependence, i.e., the vector would not change or evolve.If you're right then the problem doesn't away in any interpretation that admits of superposed states even momentarily. However, I don't know why it is a problem if each state defines its own manifold. Obviously it all becomes much more complicated but that's going to happen in any theory that includes GR.
If you're a psi-epistemist, then you might view MW as simply supplying the time-evolved 3D embedded view of a subset of all flat spacetime solutions in Wheeler-deWitt. In that sense, MW actually fits nicely with quantum gravity.
I'm sure MWers have considered this, so I was hoping someone here might explain it :-)