[OZ4]

I wasn't thinking extra filtering was the answer.

If the tube and the socket are good then it must coming in on the coupling cap or the bias line.

You did say that a cap did lower the hum when applied at the grid.

I am thinking maybe there is some weird feed back from the final section or some other source of the hum coming in on the bias supply.

With the bias supply line common for both the 27 tube and the coupling transformer center tap which is the bias to the 71s, the transformer is a good suspect.