Thanks to James and Nathan, I'm on my way to recovering the music I would otherwise lose and have paid for. A solution is apparently iLinkPod. I'm glad I live in America, where my use of that program can be legal since I already own the music. It's a shame that Apple chooses to make software so that law-abiding people have to go to such trouble just to keep what they already paid for.

Actually I'm trying this out tomorrow night so I'll let you know how it goes.