You can fabricate a steel hanger, and if you keep it to 2mm or so you shouldn't lose the innermost gear. Before going further, bolt the RD to something and see how much inboard travel is still available. In your shoes, I wouldn't shave anything off the existing dropout, because that's what your looking to protect at all costs. If you lose or fracture that, the next repair is vastly more complicated.

I suggest you work in two pieces, screwed together.

1- a hanger to replace the broken off part that lies in the same plane, as the original
2- a long, sender steel plate which if you use a decent spring grade can be as thin as .080 or 2mm, to run from the bottom of the new hanger, up behind the QR nut to near the top of the dropout. That'll give it good support and rigidity. Drill and tap the frame in two places, and the lower unit in one with the RD providing the second fastener.

It's a job that you can do yourself, with a power hand drill, a hand tap, a hacksaw (and/or jewelers saw or scroll saw), a purchased replacement hanger, or your broken hanger, and a piece of spring steel. If you want to go this route, I'll give you a piece of the material I used to make cone wrenches out of, and tell you how to heat treat it after you've prepared it.

BTW- however you repair it, make sure your repair is weaker than the dropout, otherwise the next incident will cost you the frame rather than the hanger.

If you decide it's beyond you, PM me and I'll refer you to a few shops or builders that can do the job for a reasonable price.