The high cathode voltage initially suggests that the grid was not grounded through the 249K grid resistor. Since swapping tubes fixed it, it may have been just dirty pins, cleaned by re-installing tubes a couple times. But do check the 220 ohm grid stopper at pin 3 (they are a little fragile) and the related solder joints, just to be sure.
The tube ratings are design nominal and have some allowance for individual variations - normally 10%. In your case, I expect your power line voltage is a bit above the nominal 120 volts. The supplied tubes are actually capable of more power, 22 or 23 watts being widely quoted.
If you have especially fragile or rare tubes and want to apply a lower stress to them, you can operate them as if they were 45s. At the other extreme, there are a few 300Bs with 2.5v filaments - the JJ 2A3-40 is popular - which can be operated very conservatively as 2A3s.
The driver is loaded with a constant-current source, so its plate voltage will not change with the power supply voltage. The plate voltage may drop during the first 100 hours of operation as the cathode forms more fully - that depends on the individual tube though.
