Got all the bearings and bearing cups out earlier this week! I took the frame over to a friend, who busted out each cup like it was nothing. Turns out all I needed was to place the frame on a concrete floor, with a wood block for bracing, and knock out each cup with a punch and hammer!
I mocked up a wheel and tire to see if everything lined up right, and thankfully, the wheel lines up dead even between both the chain stays and seat stays! I didn't notice it until later, but the right seat stay looks to be dented inward just a little bit. I don't know if that means this bike is unrideable as-is, but it doesn't seem to affect the alignment of the rear wheel at least.
A better look at what was (and wasn't) removed from the frame.
Not only did we get the bearings/cups removed, we also removed the seat, seat clamp, head badge and head badge bolts.
Here's where we didn't make much progress. My friend tried a number of different ways to remove the seat post, including hammering it down into the seat tube and welding this piece of angle iron on top and twisting it in the vise or hammering it from underneath. Wouldn't budge, and in fact, was ready to break. So, it looks like I'll need to soak the tube in some rust penetrant for a while, but after that, I'd like to try tapping the inside of the seat post, threading a bolt deep inside of it, and twisting it in a vice or pulling it with an axle puller. That's not going to happen for a while though, but at least I've got a few ideas on how to remove it.
With the bearing cups out, I can now get an idea of what the red paint originally looked like!
Thankfully, the bottom bracket's not in bad shape.
So, that's where I'm at now. If I can wait patiently for long enough, I should be able to get that seat post out and start building this frame back up!