You are correct, tautech. there are a total of 12 devices in the machine, three banks of 4, each bank with it's own power supply, control circuitry and output transformer.
But, I'VE MADE A HUGE MISTAKE!

I went and posted those requests on Alibaba using my regular email and the result has been spamtastic. 94 replies in the past 18 hours, all of them claiming to have the (discontinued) device in stock.

I'm going to gamble and choose one of the vendors that seem legit and claim quick shipping. I'll order 4 MOSFETs and hope something useable arrives in the promised 5 or so days. Worst case scenario, I'll be out $100.
In the meantime I'll follow your advice and study up on how to implement IGBTs in place of MOSFETs, no time like the present to learn!