Hi:
We use teflon based trailer ball grease on our mast base and ball. I also think that any grease with Molybdenum disulfide in it, such as constant velocity joint grease will be more than adequate. If you don't have your rig down, you can get the grease into the important places by slacking off your shrouds as much as possible, sticking a block of wood next to the mast base, and then levering the mast up off of the ball with a prybar. Don't pop it off the ball. Shove the grease into the appropriate area with a Q tip or something other than fingers.
No grease is gonna free up a scored ball / base combination. If your ball looks like hell replace it. Smoothing out the mast base with fine sandpaper is a good idea as well.
-Greg