Okay, the wrap-the-frame-in-OA-soaked-rags idea suggests this variant: how about wrapping whole frame in strips of t-shirt fabric, or something like that--kind of a time-consuming process, obviously--so it looks like an Egyptian mummy? Stuff some fabric in the bottom bracket shell, too. Then wet all the cloth down with white vinegar and seal the whole thing in a plastic garbage bag for a couple of days so it doesn't dry out. Then unwrap everything (another PITA) and see how it looks. Neutralize with baking soda. Dry off.
OA would obviously be another option, but I imagine that un-mummifying the frame would get OA all over one's hands and clothes. I'd worry less about getting spattered with vinegar.
I think I may try that and report back, assuming I can find enough old T-shirts.