We have C50 transmissions in the 85-86 models, and C52's in the 87-89. C50s were also used in Corollas, C52 in the Corolla GTS and the Geo Prizm. But they all have the same 0.815 5th gear ratio. Our transmission is the same, or very nearly the same, as a FWD transmission--so others might fit, esp. with some modification.
With gear ratio, smaller number = taller gear. The C transmission doesn't have a 5th gear with a smaller number than 0.725, but that's quite a bit taller than you've got. In some transmissions that's a 5th gear, in others it's a 6th. It's probably the same gear. I bet that gear fits right on in place of the 5th you've got. If it doesn't, there's a good chance a machinist can make fit into a C52 transmission.
Here's a list of C transmissions/applications.
Toyota C transmission - Wikipedia, the free encyclopedia
If you can get it to work, I might try it too.