Your drawing doesn't have separate grounds. V1 and V4 will have filaments that sit at about 13.5V, V2 and V3 will sit at about 25.5V. This is the bias applied to the tube itself, and when you try to put a cathode resistor in, you'll be providing a path to ground for battery current.
You'd need a separate cell for each 3S4 regulator, then a stack for the B+. You might be able to find a filament transformer with four 5V windings, which would help get you where you need to go.