Not sure if you see my signature but I drive on a 350 diff. I love it compared to the OEM 370 3.69 diff.
The swap was pretty easy for my mechanic friend who got my diff in his 350 and buying a 350 diff and swapping guts would be cheaper I bet than buying a 370 diff if you could find one used.
Either way I'm curious if the OP has resolved his issue and how he went about it.