There is a small PCB disc attached on top of the sprocket wheel and there are conductive and non-conductive sectors on it:
Yeah, that looks promising!
The sprocket wheel has 6 teeth and the counter PCB on top has 3 conductive sectors and 3 non-conductive ones in the pattern similar to the radiation danger sign. So I guess it should be possible to turn this camera into half-frame by making the disk with 6 + 6 sectors. But for the square, I am not so sure. Seems like 4+4 sectors will result in too wide spacing and 5+5 sectors will not be enough spacing?
Unfortunately, some counter PCBs are limited in how they can be modified. The film advance can only be changed in increments, not infinitely adjusted, so you have to get a little lucky. In this case, it sounds like you would have to settle for a pretty wide frame spacing.
As for the P&S that can be modded, there are surely some (also see my post above) but the pool of those is probably not very large. It is actually relatively easy to filter those cameras that can potentially be moddable. They should:
a) Have a sprocket wheel. If there is none, then the camera is using an IR sensor for counting sprocket holes.
b) Display the frame numbers on an LCD screen. If a camera has a small viewing window on top where it displays the frame number, it means there is most probably a mechanical system and not an electronic one.
I arrived at a very similar criteria after looking at several SLRs. The only additional one being that the sprocket needs to be free spinning. In some early SLRs, the sprocket is still geared directly to the motor, so it's actually pulling the film rather than just spinning as it goes by. Later, the motor advance was geared to the take up spool and the sprocket was just there for counting. I'm not sure how many auto-advancing point-and-shoots would have a geared sprocket.
I hope you keep exploring this idea! Sounds like a great direction to go.