"limited slip differentials" are features of the rear diff. Gearboxes have GEAR OIL in them. Once put in, they rarely get changed. Only situation I can think of is if the brass syncros are trashed then you would want to swap out old gear for new stuff.

Now, there is an additive for limited slip and Safetrak.Put it in the rear diff if necessary, just don't put it in the transmission.

I hope your rebuilt saganow is numbers matching. If it was made from trees it would be a balsa-wood tranny.