Simple mod actually works!
I used a 12AY7 for my quick test but haven't tested the others yet(exams). Swap in a 8.2 ohm resistor on each LM317 for a CC of 150mA. They end up both going to the same pin(3 I believe) and if you leave one of them alone but send the other one to pin 4(should be to ground so cut that) the shield should already be grounded on pin 9 which completes the heater/output circuit. With that setup you should only need to re-bias between tube swaps(it might not even need that really) from 12AU7, 12AY7, 12AT7, 12AX7, and a multitude of other dual triodes if you aren't afraid of air wiring(I have my tube air wired to make the tube stick out of my chassis more).
I want to play with it a little bit more because there is no reason why an LM317LZ(to-92 packaged LM317) couldn't be used in place of the 2SK117(pinout might be different). It's just a simple plate CCS with a depletion mode jfet. If this is the case it might be possible to also make this a super cheap build seeing as it would just use 4x LM317s and a couple of output MOSFETs.
Unfortunately, I might not be able to test the LM317 idea since I don't want to mess up my original. If anybody has some boards they could sell I could play a bit more.