The diff centre supported on the trolley jack is easy enough to manage along. I am assuming the car is on the ground and the diff is supported on jack stands.
I would 100% do the CV rebuild while it is apart. The difference jsut doing the King Pin bearings is huge and immediate.
Like Mudski, the last time i did the GU i rubbed back the trunnions and gave them a couple of coats of Satin Black cold gal. The wiper seals where much happier for a long time, as the piant wears over time it leaves the pits full and the wipers appreciate the maintenance.
If you were not going in to fit the locker though you could potentially continue to drive on. You live on a dirt road adn the diff has not seen a hose for 12 months. THere is not a drop in the inner face of that rim! Seems like a seep.