3a5 are very microphonic in general. It can be hard enough to distinguish hum from grounding, with hum from filament noise, with hum from mechanical vibration coupling to the valves.
If you have a transformer on the unit that vibrates for example, you will hear it amplified. One way to test that is to touch the tubes and it usually damps or changes the noise. Be careful with the voltage to the heaters - if you go past 1.6V you will burn out the heaters very quickly. Try them with a D-cell and see if the noise is gone, and you know then if its the heater supplies.
Another thing I found out is that if you are using a transformer with multiple windings - eg 150V for the B+ and then 2 x 12V for the heaters, you can get hum in the heaters. Use separate transformers and no hum. You could temporarily drop the black pcb from the chassis and just leave it sitting on its wires and see does that change it.