Just Mark-
I have some, very limited experience with 57, 59 and early 60's 3100 differentials. One, which is early 60's looked very much like the pic you posted from the rear,with cover removed, had limited slip (posi) which was housed within the housing that your pic shows has been knawed by the pinion.
I would suggest that you verify this before going much further.
Limited slips were first offered in 1959 and become more common in the early 60's.
If, as I suspect, you do have a limited slip, there will be a stack of 'clutchs' inside that housing.
Perhaps a po added limited slip from 59-early 60's to a 57 differential & it didn't quite fit.
Only a guesstimate from my limited experience.
delky dave in WYO
