[dmsfrr]

Depending on where the leaks are, fixing them with the trans in the car may be possible but not overly likely.

There are some transmission mechanics with enough experience they can disassemble the transmission in place. They're very hard to find and their job isn't easy in such a small space.
Most transmission shops these days don't even know what a FordOmatic is.
If you can find a shop that will work on it & warranty their work it's a good day.

The usual procedure is to remove the engine & transmission together.
'55 was the last full model year for the air-cooled FordOmatic, it was phased out during '56.

Mission creep is very real. While the transmission is being removed and/or in the shop, a whole list of other things will be found under the hood that should be fixed 'as long as it's already apart'.
Time and budget will likely go out the window.
.