Well, the deed is done. I soldered a piece of wire onto the magnet wire, and had a heck of a time doing so. I don't know if it's my dinky 25 watt iron, cheap chinese eBay solder, or just what or how I'm trying to solder.

But eventually I did get it. Then I bought some J-B Weld Kwik Weld ($10 at Canadian Tire), mixed a blob of that up and adhered the end of the new lead to the choke with it. Says it should set in 6 minutes and cure in under an hour. Hopefully it works.
Correction: It cures in 4-6 hours. Which is a relief since it's been 45 minutes and it's still somewhat rubbery.
