The problem is that I am trying to adapt the traditional mount for three fingers, and not just trying to start from scratch with what works for two fingers. It is not working!
Using a trad glove puppet with the arm upright it is surprisingly uncomfortable and restrictive to move the puppet arm with the index finger.
I had a bit of an a-ha moment thinking about a steadicam mounting, which might be a better model than a glove puppet. How weird is that?