You should be using a standard tranny starter as I recall. I didn't write down the casting number of the nose.....stupid me!
If yours has been too short, perhaps someone replaced the flywheel with a newer style somewhere along the way, and you actually need a longer nose, automatic style.
I will be pulling my motor out, to fit a new one, once I can get my intake/jackshaft/air cleaner issues sorted and will be able to confirm.
I just dug out the parts book for the Goose, and on page 54 there is a starter indicated "solo 289" (only 289) (I need to know what flywheel this fits!!!) as C7AF-1001-B which in the Ford parts book is replaced by C20Z-B which is replaced today by D40Z-A and is spec'd for an auto trans!!! Since your car is so early, 15th built roughly, did your car get a 289?
Further, on page 68 we find another starter listed, and this is the one I expect to find with all 302's since they used the regular Mustang/Cougar etc stick flywheel... C7AF-11001-F, replaced by C5TZ-D, "solo 302" (only 302) which indeed is a M/T version and has a shorter nose as the teeth are close to the block on this version of starter.
When using a Ford bellhousing, they had bumps in the unit that wouldn't allow you to run the auto trans unit. Only the shorter nose would fit!!!! ...until late model starters came along....then they all used the same thing! About time!!!! (1983ish and the start of the 5.0 revolution!)
Anyway, hope this helps! Haven't been here a while as I've been wrapped up in too much other stuff!!!