The MOD-3 pot mounting is less than ideal to begin with. Essentially an interference with the housing. The pot diameter is about as big as the collar on the pot that provides the press fit. Just don't get your hopes up on being able to fit any bigger pot, like from a PVS-14, in there. With L3 tubes, I've noticed a lesser "felt" difference in adjustment between a PVS-14 and a MOD-3C. The adjustment range is just compressed into a smaller span of the knob. Could replace the 250k Bourns pot that comes with a MOD-3 with a lower value pot and stretch out the gain adjustment range over a greater span of the knob. Alternatively, could also add a fixed parallel resistor to the pot to stretch out the span but the "felt" adjustment range might feel a bit "funny".
The L3 tubes reach max gain well below the max setting of the pot on both a MOD-3 and a PVS-14. Can also be safely operated with no pot or with the pigtail disconnected. Big no-no for earlier/other tubes. The L3 pigtail can also just be unplugged from the tube body.