How does a reactive ballast work?
A reactive ballast limits current the same way a resistive ballast does. V=I*Reactance.
Yes, you can use a series capacitor to limit current. Yes, if you cancel out the capacitive reactance with an inductive reactance, the net reactance will be zero, and zero reactance won't limit the current.

If you put two transformers in parallel/series as you described, it's the same as doubling the number of secondary turns. It is doubling the number of secondary turns. And it's the same as making the primary wires twice as thick. And doubling the area of the transformer core, so it can handle twice as much primary current