You'd want to be swinging 40V at the plate of the 300B, at low voltages, the mu of the 300B is roughly 4, so you'd want to put 10V AC into the tube.
This operation has the problems of:
DC compliance between the regulated supply and the 300B plate in attempting to get that much voltage output
Insufficient bias under the 300B for the required input voltage
Finding a 12V AC source to feed the BeePre (remember, stock or BeeQuiet has some insertion loss)
I would mention that a perfectly stock pair of Paramounts paired up with a BeePre or Submissive will have none of these issues
-PB