I really appreciate the advice, everyone! Makes me have hope that it's not a lost cause. Yes, it's the little set screw in the chrome wheel/knob; sorry, my user manual called it a knurled screw, so I don't know what else to call it. I'll keep trying the oil. So far I'm not having much success, but I haven't tried heat yet.
I'm just hoping and praying that I can get this screw loose enough to take off the balance wheel. The machine motor runs fine, I just need to rewire it. I can't imagine how awful it will be if I can't use this beauty of a machine just because of one silly screw!