Finally! Got it off.

After letting it sit overnight and let the penetrating oil do it's work, I followed jimc101's advice and put it in a vise to minimize stress on the frame and used dabac's advice and used a c-clamp to prevent it from jumping off.

We ended up pushing so hard trying to get it loose, that we just ended up pushing the bike, vise, and 500-lb workbench all around the room. What finally worked was we got out the heatgun, set it to 400 C (750 F) and heated up the bottom bracket and we were immediately able to get it off with no small amount of effort. It was well-rusted in place. Definitely going to use anti-seize when it comes time to put it back together.

Here's it all apart (and cleaned!):


I assume I just need to go into any bike shop and replace the two bearing cartridges and I'm good to go (correct me if I'm wrong).

Thanks everyone for all the help.