A transmission guy I met while I was on holliday once told me "Anything mechanical can be repaired , even if it is sealed, you break the seal , repair and reseal"
If its the diff , its good to get it open and have a look at the condition of the gears , internals etc and work from there . Might just be the bearings that are gone .
I agree with zippy320, take the cover off, these are usually easily accessible, check for metal shavings / chippings.
I still maintain that a reconditioned unit will be a cost effective solution, which will save you time on the repair. Unless you can find one at a scrap yard.
I am planning a trip the Cape in December, if you're really stuck, perhaps someone like Gizmo can find a good unit for you and I can bring it down.