I got a little further now, the nvidia-settings utility was actually very useful.
So, I did get a TwinView clone now, so I can show stuff on both screens.
However, this seems set the projector on permanently, i.e. I can't actually toggle it (I have to restart the X server, which is a pain). From the documentation, it sounds like what the hotkey switch does is to loop the list of modes in the metamodes. Thus I figured that if I set
Option "metamodes" "CRT: NULL, DFP: 1280x800 +0+0; CRT: nvidia-auto-select +0+0, DFP: 1280x800 +0+0; CRT: nvidia-auto-select +0+0, DFP: NULL"
Then the first mode would be nothing on the projector, laptop screen only. Then, when I first hit the hotkey, it would display both. Finally, if I hit it another time, it would display only the projector.
The first mode is indeed selected:
(II) NVIDIA(0): Setting mode "CRT:NULL,DFP:1280x800+0+0"
And my laptop screen is working. If I hit the hotkey switching button, I get the following line in my log:
(II) PM Event received: Capability Changed
but there is nothing to indicates it changes mode, and the projector never displays anything.
Is the toggling possible to achieve?