I'm more interested in how to explain our state of the art understanding of giving a reductionist account of actual physics, which seems to terminate at questions about the ontological status of quantum amplitude.

The next step below quantum amplitude, if there is one, is Tegmarkian multiverses, which are a reduction fixpoint (they reduce to themselves). (There might be one intermediate in between - I have a strong suspicion that quantum amplitudes are a continuous approximation of something discrete). However, there is pretty good reason to believe that we cannot gather evidence about them, even in principle.