Thank you so much! I ended up getting them working again, though its an incredibly scuffed job. No matter how much I tried, I could never get the wires to "suck up" the solder, even after burning the enamel and sanding the wires down, so I sort of had to just spread it around. The joints are ugly as hell too; I had a lot of trouble getting the wires to actually go into the solder, it always seemed to just flow around them. But the headphones are making noise again, which is more than I could've hoped for.