Since your experiment with shorting the grids of the output tube stopped the hum, we can say (at least) that it's not magnetic coupling between the power and output transformers. I would bet you have a ground loop somewhere.
Here's what I did to get my recent build quiet, and hopefully this will help. I had four separate ground points as follows. Now it's among the quietest pieces of gear in the whole studio.
Ground XLRs together and to case right where XLR connectors enter case.
AC mains safety ground is grounded to the chassis right where the power cord enters (or where the IEC connector is).
Filter caps are daisy chained and grounded to one point which is also the star ground for the PT high voltage center tap, the ground in the heater circuit, and 12AU7 cathode resistor grounds.
Another star ground point for T1, T2, and EQ grounds together (star) near the interstage transformer. Bypass switch grounds here as well. Bonus points if T1 and T2 are physically close together and near this star point so that their cases are effectively part of this star.
Make sure everything grounds to one and only one point.
Heaters are powered off the 6.3V winding with an artificial center tap using 150 ohm resistors. This is DC biased as per Pultec schematic, and the 62k resistor bypassed with .3 goes to the power supply star ground described above. Twisted pairs are run in twisted pairs around the perimeter of the chassis, away from any low-level signal-carrying components.
All other AC wires (mains, high voltage pre-rectifier, etc) are also run in twisted pairs away from low-level audio.
Power transformer is oriented so the 'null' of the hum radiation points away from audio transformers and EQ inductor, and also as physically far from them as the chassis allows.
Following these basic principles, I believe you should have a quiet pultec. Double-check the rectifier tube, sometimes these can go noisy as well.