I've used chassis grease on mine for the past 4 years. Rubber glove and smear a little on the ball and then on the rubber itself with a crooked finger. Works well for a few weeks. I have a water shutoff valve at the toilet so I do this without water cascading down.
I've tried the silicone spray, olive oil, CLR (calcium, Lime and Rust) remover, and maybe a half dozen others that I can't remember right now. The chassis grease works well, it's cheap, and I already carry it.
I also have carried a rebuild kit for the thing but it hasn't broken, got worse or changed in any bad way, so I just grease it every few weeks and the Mrs. is happy. I know it's not very high tech, but that's the way it is sometimes.
Ken