When run I can hear the tones changing but the sound level is really really low. I have measured the voltage between buzzer pins and it is 12V (as expected) so the MOSFET seems to be properly working.
then just put a pot where the current resistor is, and vary it until it sounds how you want it.
Do not do this because you will turn the pot all the way to the end and short out the load and burn up the pot. Instead but a 100R resistor on the end of the pot.
I fact scrub the whole idea because the resistor will not make any difference apart from reproducing the original condition when it it too high. The resistor makes a difference because it is giving the FET something to switch. The piezo alone it too high an impedance to allow the FET to actually switch.