Interesting problem in that it changes with the turntable used. I have a Garrard 301 with Ortofon TA 1000 arm and Lyra Delos running to an original CAT SL-1. It is dead silent at max volume except, of course, some normal tube hiss which is not audible at any reasonable listening level. I also have a VPI HW-19 MK IV with ET II arm and Van den Hul black beauty. It hums. Not as severe as OP's as it is not audible at reasonable listening levels more than a couple feet from the speakers. It is, however, like an itch I have so far been able to scratch.
With the VPI rig I'm using 1ft long solid solver interconnects with cotton jacket. They have no shield. Thought this might be the problem so I substituted a 1 meter pair of Straightwire ICs wasn't using. The hum got worse, however, it varied in intensity as I moved the cables around (1 meter is a bigger antenna). Ergo, it must be EMI. Note, this is a low level hum as opposed to a buzz. So it is not a ground loop. And, in any event, I've tried every ground combination I can think of and unplugged everything but the amp, preamp and turntable without success.
I've ordered a pair of Grover Huffman Empress ICs. They are triple shielded and very low capacitance. I'll post if they solve the problem.