I would clean the bearings as much as possible, and repack with whatever you use in your grease gun. Assuming you do a good job packing them, I wouldn't bother trying to add grease through the zerk until your next lube interval (I only do mine once a year, which is about 10-12k miles).
The remainder of the shaft, including the splines, can just be wiped clean. The splines will get lubed by the differential oil.
Those bearings seem to be very trouble-free in service (I've got well over 200,000 miles on what are probably original bearings), so I don't see any point in trying to extend their life with fancy greases.
However, I'd be suspicious of the ones that came off dry. It only takes a tiny, invisible spot of rust on a roller or race to create a weak spot that will gradually fail in service. And of course, any sign of roughness (preferably under as much load as you can apply) is reason enough not to use them.