you're just going to chase your tail, so to speak, by increasing the cathode R; when you do, B+ will rise to compensate.
... What if anything can I do to correct and get into a more reasonable range?
... What were the voltages like with the previous set of tubes in it? Maybe it's those tubes? (Are they real 6V6s (or are they dressed-up Russian 6P3S? - seen it happen)
Both these are right. The individual set of tubes could be a far end of the 6V6 spec range, with high Gm and higher-than-normal plate current for a given bias.
You
can bring the total dissipation down by raising the cathode resistor value. It will take some experimentation cause as you raise the cathode resistance, the (bias) voltage across it will rise, tube current will go down, but plate voltage will rise due to less drop across OT winding resistance. Which then might not reduce dissipation much (or at all). Keep raising the cathode R, eventually the dissipation will drop to the desired value. If the tubes are abnormally-high Gm, or worse yet gassy, then when you plug in a normal-performing set of 6V6's they will tend to be too cold with the new very-high cathode R.
So do try an old, known set of tubes to evaluate how different these particular ones are.