I'm sorry if this is stupid or something, but how do flea markets look in the US? Because usually in Poland you can easily buy a used (most likely stolen) bike for rather cheap at those. Or if you're living close to the border visit Germany and buy something from there.

Still, I hope you do find something serviceable for cheap in your area, and wish I could even recommend something but I literally only know that the US has garage sales and I haven't heard of much else. I dunno how alienated from your neighbors you are, but maybe asking around if someone has an unused bike you could borrow or buy could help? It really angers me that I can't help you directly and can only write this shitty comment. Sorry.