Zenith Power Transformer Connections

[Electronic M]

Sounds like a fun project, good luck on it. The LM-317/LM-337 (if I'm recalling those numbers right) are adjustable series pass regulators that can handle around 45V drop from input to output, and about 2A of current with a good heat sink. With a few in series you could have an adjustable B+ supply, and with a few in parallel with the outputs connected together through low (something like an ohm) resistors you could have a regulated filament supply (though you might need to swap the bridge rectifier for a doubler to get the voltage you want).
I've used those regulators for the power supply of my homemade audio amp, and it is remarkable the amount of hum reduction they can achieve....That amp is an output-transformerless design that uses 3 to 4(4 for more power) 6080/6AS7 output tubes per channel....That's in 4.0 surround mode, I switch the unused rear channel outputs to be in parallel with the front channel in stereo mode giving 8 per channel.

If you have problems with line voltage fluctuation causing blooming on your TVs you could use that self regulating CCII transformer and another transformer to step one of it's secondaries up to line voltage (if it does not have a 120V secondary), and use it as a regulating isolation transformer for one of your sets.