At a minimum, I would try turning the shafts with my fingers, to feel for any roughness. Probably I would also remove the center section to inspect inside, clean out any dirt that may have been carried along with the water.
While certainly not trivial, I'd say doing a diff is easier than a gearbox or engine, for example. You'll need some unusual but readily available tools (dial indicator, 1" micrometer, bearing separator, hydraulic press, 1/4" torque wrench etc) plus a few specials that you can easily make yourself (mostly brackets for holding things). Getting the contact pattern right is the most tedious part (assemble, check pattern, disassemble, change one shim, lather, rinse, repeat ad nausem) but with any luck your new bearings will match the old ones close enough that the original shim packs will be right.
Here's a few photos (not in order) of my Stag diff, just to give you some idea:
https://s258.photobucket.com/albums/hh260/TR3driver/Stag%20diff/