Here is a possible answer. It doesn’t require AE or anything other than what comes with MC:
Open QT with alpha file in AVID FX through MC using FX title matte effect.
Open FX GUI, delete second video track, export clip as AVI using defaults which has alpha. Pretty quick export, it seems.
Bring it back in to AVID FX as AVI, now with alpha.
Now all clips are AVI and all limits, either as to file format or standalone/tied to MC are solved.
This is working for me. Please check it out and report back.