I rotated the three 12AX7 one more time and that did it! The hum is completely gone and it's very quiet. Does that mean that one of my pre-amp tubes is going (or gone) bad?
Well, maybe they weren't fully in the sockets. Or maybe there was some oxidation on the sockets or tube pins that was scratched off.
But one thing that is normal is that there is some amaount of leakage from the heater to the cathode. That leakage maybe be exceedingly small, or it could be just moderately small. If there is leakage, it may result in hum being transferred to the cathode, and if the signal is very small and leakage is high, you get audible hum.
So the best plan is to use low-leakage tubes in the earliest preamp stages, where signal is small. Tubes with leakage too great to use here without hum might be successfully used in stages where the signal level is much higher, say, a phase inverter.
And think about the tweed Bassman. The enormous 250uF cathode bypass cap is not only about insuring full amplification down to the bottom of the bass range. It was also about shunting any leakage that occured in that first stage to ground. The 12AY7 was also used because it was developed (and at that time, advertised) to have low leakage and hum.