With the cathode at 20.7V with a 470R, you'll have 20.7/470 = .044A (44mA) tube current
And if the plate is 370 and the cathode is 20.1, then you'll be dissipating (370-20.7)*.044 = 15.3W! (including screen) You want to aim to get somewhere between 12.5W to 13.8 W (assuming you have a modern brand of 6V6)
So you need to get the plate voltage down a bit (say to about between 340 and 360). Best way is to to lower the B+ by putting in some reverse-biased zener diodes in series with the HT winding center tap to ground. Try a couple of 12V 5W diodes in series. (Make sure the banded end is pointing to ground.)
Incidentally, What brand of rectifier have you got? Some '5Y3GTs' are not 5Y3GTs if you get my drift.