My Newton's case that is. It seems that the current wiring is more or less ok so I screwed everything back together. The Bluetooth module is powered when the Newton is on, and it's off otherwise. I still needed to figure out a reset method for the module since the two power lines are independent. There is this practical serial channel 3 select signal on the internal J6 connector which works nicely as a reset line. Now whenever the Newton reboots or is powered up, I reset the module. Power consumption is great, when active, the total is always under 100mA.
An alternative to this would be to power the module all the time and use a voltage regulator to get the 1.8V out of the permantently on 3.3V line. Maybe another day :)
But there is still a Heisenbug in the whole setup. I'm not exactly sure if the channel 3 is up to speed or if I really should get the RTS/CTS handshake working, for now I have to use a Wait(1) after each HCI packet. That's a minimal overhead. Would be nice though to know what's going wrong.