Thanks for this! Heater voltage is right at 6.3v. I've been thinking that this is a tube issue because the noise generally goes away for anywhere from a week to a month after installing a new tube, it has always come back either intermittently or consistently after a while.
However, it's certainly possible that I've been looking at the wrong thing, so I can try isolating the noise to another element. I'll swap out the capsule with another good M7 that I have to see if by chance it's the capsule, but this is a new Thiersch Blue-line M7 which (I would hope) isn't failing already. But I guess it's certainly possible.
The coupling cap is a Mundorf Mcap, and all other caps are new, high-quality film types. For the moment, I'm going to undo what I did a couple days ago (putting in the bias trim pot and the 600pf cap from plate to ground), try to get the plate voltage to spec, and see where that gets me.
Thanks again for all of the suggestions!