The S.E.X. already has DC heaters so there isnt much you can do there. Referencing the center of the DC supply to ground helps remove a lot of hum if you have not already done that tweak. Second point of attack for hum reduction is the HV supply, i found a 10H choke sorted that out rather nicely. I have documented both in my rambling thread..
I had thought about shunt regulators too for the HV supply, but i don't think there is the voltage headroom to allow for that, certainly not with the solid state setups i have used in the past which will need 30-50volt overhead to operate properly. I also have no idea of the current limit of the HV transformer as that may limit options too. Again the Salas and K&K regs i have used need to sink at least 20ma more than the load.
I also briefly tried the 6SN7 in the S.E.X, admittedly i didn't modify the operating points i just plugged it in and started testing, the results was so awful it didn't last very long. If you want to use 6SN7's just start again and build another amp around them, don't ruin a perfectly good S.E.X. amp

Sorry if this is all sounding a bit negative. Here is another idea, use the iron and convert it into a stereomour as i believe they used the same iron, or even better just buy a Stereomour II and modify that into a headphone amp. I know it sounds crazy but i am currently building a "big tube" speaker amp for 2A3/45/300b style tubes as i had never used them before. Currently using the Russian 6C4C tubes which are a Russian 6A3/6B4G, which is a 6v version of the 2A3. I am heating mine with Rod Coleman regulators via dual filament transformers, the rest of the amp is basically a dual monoblock setup, two mains transformers, HV supplies, shunt regulators and CCS loads for the driver tubes. For the output tubes i am using a bunch of Bottlehead/magnequest iron i picked up second hand so its not a million miles away from a Stereomour. The thing sounds so good, and is so quiet i am currently using it as a headphone amp with my HD800's. It is hands down better than the S.E.X amp, and almost as good as my shunt regulated 6C45 based amplifier. The 6C45 has a hair more detail and resolution, but the 6C4C sounds more natural and realistic. I recon when i put some money into quality coupling capacitors it will trump it and become my main headphone rig. Surprising really as that was never the intention when i started building it.