I dont work for a transformer manufact, but I get involved with industrial controls, what you mention I think is what in industry is burst mode power control, where you switch a full cycle at a time, and omit cycles to reduce power, this I had thought of, but for me I'd have to use a pic to do that.
A cap might do but it'd need to be big, the secondary current is around 50a, so that would need some need hefty devices.
I managed to find a internal pic of a burnystar pyro machine, there is a pcb in there and a trans, theres only 5 or 6 discretes on the pcb, doesnt look as though theres a load of smd's on the back, so with this in mind I bunged a standard dimmer on mine, and connected the pyro tip and let it soak for an hour, the trans got warm but not too bad, the dimmer was a little warmer but seems ok, so I might go with that.
Now having looked at the dimmer it says on the back, transformer output 250va and theres a diagram of a trans connected pictorially to the terminals, maybe this dimmer was meant for transformer low voltage lighting.