Things still work if I remove the -120V and just use the pot as a variable resistor to GND, but then if the oscillator fails to start the 504's saturate with current :-/.
In this case, the pot is acting like a variable grid leak resistor, which needs the drive from the exciter to create the bias voltage on the grids. No drive and the plate current will more or less run away with no control.
As far as the modulation arrangement goes, your blocking cap on your modulation transformer is on the wrong side from every arrangement I've seen, it would be on the side that is connected to the choke, not on the grounded side.
Your screen dropping resistor is also in the completely wrong place, as the schematic is drawn, it appears that you would be feeding RF back into the tube on the screen, you want to have that screen dropping resistor connected between the power supply side of the plate choke and the screen of the PL504s, not the tube side of the plate choke.