You'll need to check all of the Diodes in that circuit and make sure they can handle that, as well as change the Filter Caps to 50v, as they're only rated at 35v. You could prob push it to 30v without any other modification, but any more than that and you'll need to swap at least the Caps out.
The POT is used as a voltage divider, so 10k, 100k or 100M it's going to work exactly the same way.
If they made the thing right the gearing shouldn't matter at all as it should use feedback from the POT to know where it's at. That SEGA cab that he did using the Logitech Wheel would be the same deal as here, since it's geared similar to the 360 wheel and he didn't mention anything beyond having to turn the FFB down some (naturally, going from that stock motor to the monster he used) so you shouldn't have any issues going from the geared setup to a pulley setup if you decide, just keep a small pulley on the motor and a larger one on the Wheel.
The gearing is used so a smaller and cheaper motor can be used, while still getting decent torque from it.
What I was thinking was to make up a small PCB to carry the driver ic and its associated components, all of which would be rated high enough to handle the 36v. Then for power take an appropriate PSU and feed it directly to the new driver pcb. To power the main board I would take a feed off the 36v psu and drop it down with a voltage regulator to around 20/24v.
I've just got back from taking my daughter to McDonalds and spent the whole time wondering if the processor is using the pot to reference center wheel position. If that's the case - as you mention above - then changing the gear ratio to the FFB motor and altering the degrees of rotation should work out fine electronically.
A smaller gear and bigger motor like the Happ wheel has should make the FFB have a quicker response shouldn't it? I've just had a quick go on Forza and noticed when I let go of the wheel it returns to center quite slowly.