Dr. Slack wrote ...

We call that a parallel capacitor, not a series capacitor, in engineering circles. The capacitor is connected across the transformer output terminals, and you're measuring the voltage across it.

A series capacitor would be connected in series with a load, and you'd measure the output voltage across the load.

With a K1 of 0.99, there's very little leakage inductance. If you want to model the shunts of a MOT, then decrease this value. Try setting K1 to 1.0, to see whether a transformer with no leakage is much different. Setting it to a lower value will decouple the secondary inductance from any shorting effect of the primary and supply.

You appear to be resonating the primary/secondary inductances, with the 0.5ohm primary resistive ballast failing to short circuit these. This was probably the defect in my thinking, the presence of the primary ballast. Without it, the low mains supply impedance would short-circuit both primary and secondary inductance, leaving nothing to be resonant. Try the simulation again with zero ballast resistance to check whether this is the case.

I think there is a way to factor in the core magnetics, but I've never done it myself. Try google. There's plenty of interesting insights to be gained from this simple model without worrying about saturation. You can mimic saturation very crudely by decreasing the inductances.