Well, the lock wrench arrived, and I managed to open things up. As expected, it was pretty gunky and gritty. Once I cleaned everything up, it looks like I just need to re-grease and re-assemble.

I could not manage to get the fixed cup removed (I applied some penetrating oil overnight, and tried using a vise, as wel las the Sheldon Brown bolt/nut DIY tool). Since the fixed cup looks fine, I am planning on leaving well enough alone.