I might also go with a lower value pot then 500k as well but shouldn't make a difference. I tend to let the tube breath a little, make some heat.
You could power this using two 6v transformers plugged in series. Pull the heater off the 6v after the first transformer and then step the voltage back up with the other transformer with the secondary of the first transformer connected to the secondary of the second transformer and send that through a full bridge rectifier. I might also increase the two coupling caps to maybe .03. Keep in mind, you are going to see some gain. Perhapse too much. That could be reduced by lowering the plate load resistor, the 100k, attenuated with a simple voltage divider or that pot.