When I turn the dimmer to the off position (max resistance), the bulb
turns off completely. Does the lamp still use power in this position?

If it's not too much trouble, I'd like to fix this "right". Is there
any reasonable chance that I could find a 300K ohm pot with integrated
switch that would fit directly onto the circuit board? If not, where
is a good place to buy a 100W 120V dimmer module?


Yes, it may still draw some power, but very little. You could check it
with a multimeter if you wanted, just use the AC amps function and wire
the meter in series.

I've seen the dimmer modules various places online, personally I'd just
install one of those inline switches on the cord near the lamp.