just thinking out loud but what happens if...........

you freeze tracks in BIAB
open the file in RB - tempo and bars should match
delete all the regenerated tracks (which would leave the chord sheet and part markers i think!)
re-open BIAB and select DAW mode and drag and drop the frozen tracks (and multi style changes) into the RB song...........

would that work? you'd still have to add reverb etc to the tracks in RB but would that be a simple workaround?

can't see any need to go back to BIAB if it works