I think my 727 is fried. Now I'm at a crossroads...

you might have to adjust idle, you could run the same cam after the swap. For the record im in my 50s,been driving stick cars daily for over 30 years even my little Ford Commuter car is a 5 speed Focus sedan. Stick is always reliable and affordable. But, I dont know is there a reputable 727 guy or reman house?

I would think these cores have been built more than 3 times now maybe there are issues such as stresses aluminum casings etc that just aren't caught during the rebuild.