> can you make a voltage doubler with tube rectifiers?
Sure. But look where your cathodes wind up. All different voltages. If you use naked-filament cathodes, you will need extra heater windings, well insulated. If you use heater-cathode rectifiers, you need very good heater-cathode insulation.
Also, voltage doublers either run tubes in series (multiplying plate-drop) or run the caps half-wave (increasing the peak/average current ratio and stress, with enormous resistance-droop).
That's why 99% of hollow-rectifier schemes use the center-tapped high-volt winding. Even though it needs more labor in the transformer, it use a single-cathode rectifier. Two plates on one cathode is a lot cheaper than many cathodes and heater windings.
There are a few exceptions. I have seen US market TV sets and radios running 250VDC from 110V voltage doublers. At 250V, heater-cathode insulation can survive, requiring just one heater supply. At TV set power, rectifier costs are huge any way you do it, and running the big H-sweep tube at higher voltage improves its efficiency enough to compensate some of the rectifier cost. OTOH, while there were volt-doubler radios and even (hot-chassis!) guitar amps, improved low-voltage output tubes soon made such drastic plans obsolete.
Taking some power from the middle of the full-wave doubler is trivial and often done. In fact when crystal diodes grew to the size that they could handle the stress, the FW doubler was a very common scheme. Especially for 6550 and 8417 output tubes where the G2 likes to sit about half the plate voltage. Done in the Bogen and Dynaco 8417 amps and in the monster 4x6550 servo-amps in the Ampex Quad VTR.
Regulating tube audio amps is, In My Humble Opinion, silly. (With a few specific exceptions such as vari-Mu compressors, and regulating the Screens of high-power amps.) Tube-regulating is extra silly. You have to make too much power, plus a little extra, and waste much of it. The extra power and heat and cost could do more good in other places. A tube regulator is another audio amplifier, just optimized differently. The extra iron needed to cover plate and heater loss alone would (in a rational world) buy a LOT of cool choke. Getting a low-low output impedance, or even high ripple rejection, is not at all easy. Just because the sand-heads regulate at the drop of a 7805 does not mean it is a good idea in the tube world. Good tube circuits will work fine with about any voltage they get, as long at it is clean (and chokes/caps do the job with little waste). But that's just my opinion.