Well, I think I may have fixed it.
I am not a very good mechanic, to put it gently. I have been trying to drill out an inconveniently placed stud that holds the exhaust to the engine block. It is the first time I have drilled out a bolt like this, so I am cutting myselfs some slack. I will admit that our resident scooter repair expert and shop teacher would be ashamed of my poor workmanship if I was his student. But nonetheless, my incompetence is matched by my persistence and I got the thing drilled and the new stud installed, and I am ready to put it back together once I pick up a couple of nuts and washers that I need.
I have no idea if this is actually going to hold. But I tried.