Drew,
I don't want to speak for those who have been working with this amp for years but I believe that the answer is no. At least not easily. You could tap into the 12.3 AC filament and build a rectifier, but the transformer may not be able to supply the current to the stepper motor and the 12AT7 at the same time. The 12AT7 takes ~300mA. Stepper motors can take a lot of current, depending on the amount of torque they supply. Also, you may not have enough voltage. the 12.3AC has a 17V p-p that you can rectify but as soon as you pull some current from the regulator you just built that 17V will probably drop below 16V. You could also use a voltage doubler from the 12.3VAC output and drop the voltage down with a regulator or resistor, but again you may not have the power available. You could also draw current from the 400VDC supply using a large high power resistor, but this may affect the power to your output tubes. I don't know the current rating of the HV supply. I think your best bet is to add a small switching power supply inside the box specifically for the stepper motor. You can just tap into the 120VAC main. This is just food for thought and I am sure PJ may have a more complete answer.