I put a transmission on my project 84.  It quickly went south.  It
started slipping and wouldn't move.
At this point I didn't hear the whinning noise while going over about
15mph.

I put a second transmission on and it shifts strongly.  But as I get
going a whine developes.
It almost sounds like tire noise but when I let up on the gas while
still going the original speed
the whine goes away.

It's not a real high sound.  It really sounds sort of like badly worn
tires.  My tires aren't worn.
Also the sound is clearly coming from the back.