Good luck! Obviously this only works on a bike with an open BB shell, but I've been thinking about how to grip it from the top. For the bearing cups, most people I know drive them out with a 2lb hammer and soft metal punch--aluminum or brass. Things might go easier if you lay the frame on its side and support it adjacent to the shell. You only need enough space between the frame and floor for the cups to pop out. The cups are just a press-fit, so don't be afraid to wail all around their perimeter.Awesome, I'll give it a shot! Thanks for your help! I've got just the tube to use for this. I'll probably want to remove the seat post after I remove the bearing cups though, so I'll have more room to work with.
Once out, I second the use of citric acid to bathe rusty loose parts. It's safer than some of the other products and you can adjust the concentration by the amount of powder you use. Not the fastest, but it works.