Thanks, one and all!

For the screw hole that is simply stripped, the dowel idea sounds good. As for the screw hole that has a crack running right through it the situation is more complicated, as the crack crosses a glue joint and propagates a few inches along the underside of the instrument. I'm awaiting advice from Andy Cohen, but I may well resort to professional help. The hitch pin guard also houses the Marxophone keyboard, so I am eager to resolve this. For now, I have found I can clamp it on as a temporary fix.

There are indeed very similar related instruments, the celestaphone among them.

Thanks again, and be well!