The paint idea seems to be working. Hasn’t stood the test of time yet, but the mirror orientation is now solidly staying where I put it.
I used black Plasti-kote spray paint. Sprayed a little paint into the spray bottle lid, then used a small artist’s paint brush to paint all the parts of the ball I could get to by rotating the mirror. Three coats, letting it dry an hour between coats. Noticeably harder to move, but mirror still remains moveable, and when properly oriented, faithfully staying in place. If it starts slipping again I think I’ll try the same paint method but add a little fine-sifted sand to the paint to give the ball/socket interface some extra friction.