OK, that is definitely 120Hz hum which implies it is getting in through the HT supply. The fact it becomes lower when you short V1 pin2, which is the second stage grid, is further evidence of the same. Let's try improving the HT supply to the first stage. Replace R3 with a 10K and 91K in series, with the 10K connected to the HT supply end and the 91K connected to the V1 pin6 connection. Then connect an extra 22uF 450V electrolytic from the junction of the 10K and 91K to ground. This will slightly reduce the gain of the first stage but mostly add some extra HT decoupling which should reduce the hum.
Cheers
ian