[hemi43]

Don't refill the diff yet !!
If the U-joints need replacing, you'll have to drain the diff again to remove the axles.
If it was me, I would take both hubs apart and see where it's binding.
Take the large pin out of the differential and remove the spider gears. This will allow you to spin the axle shafts independently of one another so you can see which side causing you problems.
That milky diff lube has definitely been contaminated with water, so you need to decide the next step. Hopefully the water came in the vent hole on top of the housing, or it went by the axle seals. Unfortunately, the axle seals are located inboard and the whole carrier has to be removed to change them. Not sure if this is something you want to take on, but if you do we'll help you through the process. It's not difficult, but you will need a few specialty tools like a dial indicator and a seal installer.
At the very least, I would replace both U-joints and check the locking hubs for signs of damage because that's where I think your problem is.
Dan