I put that same transmission in my .53 F 100. I swapped the original 3 speed input shaft into a thunderbird OD transmission and everything fit fine. Just make sure the number of teeth on both input shafts are the same.
I know this is an old thread, but my question is why shouldn't you run power straight from the battery to the relay? Why use the starting solenoid instead? If you put an inline fuse, aren't you ok?
Thanks.