Electrical – I have a Transformer Core – need help with winding/calculation

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

Consider adding an automotive light bulb in series. Something like a 5.75" '12 Volt' round headlight bulb (high+low beam both connected) would be about right. They are about 100W total (7A or so) and designed to operate from about 14V continuously so they should last forever in this service.

As a bonus, the light will indicate when you are current limiting. I still have a beater that uses these things so I know they are still available but getting a bit rareish.

The connections at the back look, as far as I can recall, like regular 1/4" (6.35mm) fastons but if not they are solderable brass. Or grab the bulb and snip the connector from the nearest automotive junkyard.

The bulb is a highly non-linear resistance so during normal operation the voltage drop will be very low, and most of the voltage appears across the brush and surface you are working on. If you short it or come close to a short, then the bulb filament temperature increases and the resistance will increase by an order of magnitude or so, so the circuit is protected.

Edit: SAE drawing with connections shown from this source (connect the upper and lower filament terminals together).