Before you decide that 3rd is truly toasted, check the shift collar first... mine was broken and it would lock between gears, somehow it was still driveable though.
If you take the front half of the case off first, almost all of the internals should still be attached to the center plate, it should be better for documentation and procedure purposes. I haven't taken an ax-5 apart myself, but I saw mine disassembled at the tranny shop, and have read extensive rebuild materials through the FSM's, seems like a pretty basic transmission, but the biggest problem is the botched overdrive gears.
Has anyone researched on whether toyota transmissions have any swappable parts for ours? Being Aisin-warner and all, I can imagine that some of the cousin transmissions in tacoma's, t100's, and supra's are at least similar?