The answer to the original question lies in the layout of the power supply module. Without that, I cannot advise on the best powering option for this unit. If you can get that schematic, I would be interested in seeing it. My guess is that there is a filament regulator circiut there. What it needs for an input I can only guess without a schematic. One thing for sure is that it would certainly need a constant current output. If the filament current is excessively low, then the cathode will be starved, thus decreasing the tube current. If the current is too high, then there is risk of damaging the filament or at least decreasing filament life.
And yes, the plate voltage is higher than the capsule voltage since there is a 500K res. in series with the cap and 200K in series with the plate.
As to the ac vs. dc issue, isn't the filament electrically isolated from the cathode-therefor not in the signal path?
I deal with tubes every day, but they are much bigger, have 150 KV across them and emit X-ray.
Thanks!