Any shielded cable in the amp, from the input jack to pin 2 of V1 or any where else, should only have the shielding connected to ground at one end. The other end of the shielding should be trimmed short and covered so it cannot contact anything. Connecting both ends will create a ground loop that will induce hum.
Also, the “twisted pair” of the heater circuit needs to be tightly twisted the entire length, including between the sockets. And the heater circuit wiring needs to be away from the other leads.
Check out this link: http://www.freewebs.com/valvewizard/heater.html
Read the section on “layout/ lead dress”.
Single-ended circuits have a reputation of being noisy but the 2Stroke can be very quiet. When demo-ing my new 2Stroke head, one of the common comments is how quiet it is.
If that was my amp I’d:
1: rewire the 6.3v twisted pair
2: shorten the leads throughout the amp as much as possible
3: confirm that the shielded cable(s) are only grounded at one end.
and then see where I stood.