... rather than spontaneously arising in different independent populations (which has always been where my skepticism of the multi-regional hypothesis).
I think you have the Multitegional Hypothesis confused with something else.
A pattern of interwoven or braided genealogies however does provide paths for sharing different traits across many areas creating a montage of mosaic patterns.
Multiregional evolution holds that the human species first arose around two million years ago and subsequent human evolution has been within a single, continuous human species.
This thing you're talking about involving independent evolution of identical characteristics in unconnected populations isn't MH.