+1 on moving the PSU to an external box, or perhaps try a toroidal transformer, you can find them for tube preamps with both HT and filament winding
The wires going to the 6J7 grid cap should be shielded. The old amps even had an additional metal cover that clip on the tube to shield even the exposed connection
Have you checked the resistance between the 0V bus bar and chassis is very close to 0 Ohm ?
Personally I would rather connect the 0V bar to chassis on a bolted solder tag, instead of the xlr connector tab.
And also use a dedicated grounding lug for the mains earth bolted to the chassis with a locking nut, to avoid the safety earth become loose.
Also check the polarity of the filaments is the same on all tube sockets.
Have you actually measured is 60Hz and not perhaps 120Hz ? In that case the HT power supply might need additional filtering