As a GMMP user, I can manually trigger GMMP to generate a stats.xml, and I can manually copy it to anywhere I want to, be it the sync app's directory on the phone or anywhere in my PC.
So I imagine possible solutions would be:
a. Add an option in sync app to look for stats.xml in its own directory.
b. Add an option in Musicbee to load up stats.xml inside the PC.
But since I'm no programmer, I'm not sure if either of the methods are implementable, or that they work at all.