It turns out you were right about the "common cathode connection" While technically you can do it, the current source will be fighting the antiphase signals of either tube as well as the different tolerances of the tubes and you will not end up with constant current at the cathodes.
On the other hand it doesn't matter because the current sources will make sure they are both running at the same current anyway and maintain balance. Even with different tolerances the balance will be the same since both current sources will be individually ensuring that the tubes operate the same.
As for the force balance mod you would have to splice apart or rip out the copper trace between the cathodes in the input stage for it to work but it's not hard to reconnect them whenever.
So I was thinking, if you cant keep the "common cathode connection" with the current source because it would be fighting anti-phase currents then what does the situation look like when a single 1.5k resistor is fighting the antiphase currents?
This is our stock input stage with the 1.5k tail.
This is what the voltage swing looks like with this
Almost a sawtooth wave.
The current swing through each tube seems fine
Now let's see what happens when we separate the "common cathode connection" independently bias them.
Let's take another look at the voltage when the two were connected
and now when they are separated
Much better until you realize the voltage swing of the top one is a couple milivolts and the bottom one is hundreds of milivolts.
This results in lower current and voltage swing at the cathode and anode because the voltage swing on the separated version is following the input to an extent, meaning there's less cathode-grid voltage differential, meaning the tube is not turning on/off as hard.
The reason the "common cathode connection" is maintaining a stable voltage must be due to the constant antiphase currents canceling out changes in voltage.
So it seems that the balanced design has a unintended bonus of creating a stable voltage reference.
Although you get more gain by having a stable cathode voltage, using a single resistor for each tube generates its own local negative feedback so it could still possibly be better.
Another option is a current source for each cathode but that is another can of worms.
So if the cathodes have a stable voltage reference via the resistor then another option for that route is a LED biasing, yes as in
They are constant voltage devices and are often praised for superior sound to resistors, they are often used in input stages.
You'd want to use an infared LED with a forward voltage drop of 1.5v and strap a 4.5k resistor (depending on max current of the LED) between cathode and B+ so it has enough current to maintain linear voltage regulation.
Will this resistor affect tube operation? No, the excess current will flow from ground to B+ and voltage will be maintained.
The last option is also highly praised, perhaps more so then the LED option. It is often considered very musical.
It is battery biasing.
Yes as in this
Batteries are also constant voltage sources. If you connect the positive terminal to the cathodes and the negative terminal to ground it will maintain a constant voltage and many people like it for its musical sound.
Different battery types sound different, lithium/alkaline/life/etc,etc, all have their own sound.
There was a contest once in vegas and the winner was some sort of phosphurous airliner backup deep cycle battery or something, in any case you can "roll" them like tubes.
Luckily 1.5v batteries and battery holders are everywhere.
Another voltage source is a solar cell, as far as I know it's never been tried but I have a stack of cells I got on the cheap for a rainy day.