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You don't necessarily have to use a ballast to do series tube heaters, and you don't necessarily have to have the perfect transformer either.
I would at a minimum use an isolation transformer for the power to prevent having a hot chassis. You could probably find a beefy generic 120V to 6V power transformer and a 120V to 240V (a 240V to 120 will also work if you swap primary and secondary)....Hell you don't even have to buy new, there's plenty of used options and they're usually MUCH cheaper. A voltage doubler rectifier circuit can work for higher B+ from a lower voltage transformer...Many TV makers did this.
If you want to do series tube heaters you don't need a ballast... plenty of series string TVs didn't use one. The trick is making sure all your tubes have the same current rating and having enough that the sum of the voltage drops is somewhere in the 110-125V range.... there's other tricks like if you need to use 2 tubes of half the current (with identical voltage across the 2 low current tubes) you can put them in parallel. If a low current tube isn't half the current you can often come up with a parallel 2W resistor that'll compensate....It's all ohm's law, KCL and KVL maths.
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