...the heaters for V1 are copied from a Mesa schematic...
In Merlin Blencowe's book, he talks about a buzz problem caused by rectifying an AC heater winding into DC. The problem is that the (rectifier) diodes flow abrupt, short, bursts of current, and this puts "notches" in the AC waveform of the heater winding.
Sharp features like these notches represent relatively high frequencies ("buzz"), and because the heater winding is on the same transformer as the HT, this buzz now shows up on all the transformer windings, and can make the whole guitar amp buzz.
I can think of a few ways of testing if this is the source of your buzz problem. Perhaps the easiest one is to temporarily disconnect your V1 heater power, and then use an external DC source to temporarily power V1's heater. A 6 volt DC power supply, or even four "D" cells in series would do. If this makes the buzz go away, you have your answer.
Compared to the old-fashioned "four diodes + big cap at 60 Hz" approach, one of today's cheap little switch-mode DC power supplies is far, far, far better at providing clean DC heater power. Even for a single 12AX7, it takes a LOT of filtering to supply clean DC using the old-fashioned approach. A single electrolytic cap won't come near what you need.
Marshall engineers didn't have the option to use a cheap little SMPS for V1 heater power back in the 1960s, because they didn't exist back then. But you are lucky, because you do have this option now!
You're unlikely to find a 6.3 VDC switch-mode power supply, but there are a few options. The simplest one is to just run a 6 V DC power supply, which you can buy. Or get a power supply rated for a little more voltage - 7.5 volts, say - and put a resistor in series to drop the voltage down to 6.3 volts at the tube heater.
Of course, you also have the option to wire V1 to use 12.6 V DC heater power. You can use a 12V DC power supply, or a 15V supply with a series resistor. I've even seen 13V DC power supplies, though I don't think they're common.
-Gnobuddy