Update. Pulled the water pump again Thursday night. (Wife is out of town, can tinker on cars every night. Is this good or bad?) I'm getting better every time - 50 minutes from a complete car to having the pump on the bench.
Checked the mating surfaces; they looked good. Cleaned everything up with a degreaser, removed all traces of grease from the pump, flange, and o-ring. Put it back together dry. It was perfect, right from the start. My problem was too much grease - it doesn't take much to cause a problem.
The shop manual doesn't say to use grease or anything else. Given the snug fit of the o-ring in the water pump, I think that's the thing to do.
Gotta love that hard earned success.