1993 Ford F 150 93 4x4 W 302ci V 8 Automatic Transmission Shifts Fine Forward

I have '93 F-150 4X4 w/302ci V-8. The automatic transmission shifts fine in all forward gears at all times. It will only go in reverse when cold. After being warmed up, when trying to back up (in reverse), it's like the transmission is in neutral - it doesn't move. Also, if I need a trans rebuild, to save $$$ can I use another '94 F-150 auto trans attached to another 302 but in a 2-wheel drive format? Something about swapping tail shafts? Thank you.