I was able to get it fully disassembled yesterday and was initially a bit taken aback by the amount of rust present. However, it actually cleaned off very well. I washed everything with some water and antibacterial kitchen spray which removed probably 80% of the rust and dirt from everything. The PCB is still stuck to the backplate since the two screws holding them together were too rusty to remove. I removed all of the hammers and barrels and placed them to the side. Everything is now taking a bath in some rust removal solution (which is completely safe for use on as plastic).
As for the metal components, I'll be lightly sanding them and then spraying them with antique nickel Rustoleum in order to prevent any further corrosion. The barrel plate is actually immaculate other than a couple of light scratches, but I'll be painting it too since there is some bare metal exposed. Hopefully I'll be able to get the remaining screws out once I pull them out of the bath so that I can finish cleaning everything completely. The internal springs for the feet on the case must be in pretty good condition despite the rest of the keyboard since the feet work perfect and there's no spring noise.
I also have the barrels, keycaps, and hammers soaking to remove as much of the rust and discoloration as possible. The plan is to remove the remaining bits of springs still stuck to the hammer stems, and then replace all of then with good condition Model M springs. The foam is in really good condition, but I might consider replacing it while it's already open. All in all, I'll now about $30 into this project after buying the rust removal solution, a plastic bin to soak everything in, and spray paint. I think there is a very good chance of getting it all working again so long as I replace the controller.