What is the voltage of LED string when not conducting?
So when I switch off the bottom MOSFET, is it going to see a) zero volts b) 120 volts c) something in-between like 120V - 20 x 3v (effective zero current forward voltage) = 60V?

I would say 120 Volts, when the LEDs are off you basically get a resistive voltage divider of all the LEDs in series against the off resistance of the NMOS. I'm quite sure that the NMOS will "win" (have a higher resistance) so the voltage will develop across the NMOS.

Note that since no current flows, the LEDs will behave as a resistor and/or leak some current. And no current can flow as the NMOS prevents it.

The LEDs will not be able to drop the voltage as for that, some current would have to flow, which the NMOS prevents.