The switched 3.3V line works. I hope it doesn’t cause any long term problems. Now the module is powered whenever the Newton is switched on. It takes under 10ms for the module to get into stable state, so switching it on and off is not really a problem.

Somebody with the skills to solder the dongle killer should be able to wire the BT module as well. Of course, a ready made module like the SER-001 would be much nicer!