Damn, so it really was the old school real deal huh?
Ah, mains isolation transformer? Crude, but I guess that'll work.
Geez, that thing must be, well, everything must be massive, really. What did this all fit in originally, one or two racks worth?
And 50A circuit? Nice.
So it will be DC output? I was confused because you said pulsed output earlier. But then why would the user control the inverter frequency, that's internal, who cares..?
So, if I understand this right, your problem is the transformer, and IGBT control. It can't be a fixed chop, it has to adapt to load.
The SCR stage won't respond nearly fast enough: 26.4mF is a fuckload of energy (2.7kJ at 320V!) and, just do a ballpark smell test: if your TIG torch is doing 20V at 100A that's 2kW continuous, or 2kJ/s. The SCRs could fuck off for the better part of a second and you wouldn't even know anything's different at the other end. Yup, smells alright!
Sure you don't have to use all the caps, but the inductor's going to be a respective value, and you'd prefer to shrink both at the same time. Changing the inductor is a much harder affair. Removing capacitance raises the supply impedance and output ripple, which is probably suitable here, but only to a point. (That said, if the choke is of suitable construction, maybe you can just reduce the airgap: this increases inductance and reduces saturation current ~proportionally. Likely you don't need but a fraction of its original current rating, either.)
Yeah, SCRs in and of themselves are capable at mains frequency -- maybe even up to a few kHz depending. That means they're good for regulating output against variation in mains voltage, even fairly sudden changes. But that's not the problem, it's the filter after them. And you can't make it too small because, well, it's gotta ride through the 120Hz rectified waveform at least, but will need a cutoff frequency about a tenth of that to get reasonable output ripple. And a 12Hz cutoff frequency is pretty slow -- you will literally feel it in the pedal response, or how the arc stretches and breaks.
So to maintain arc stability, regulate current versus arc length, control arc current at all -- you need PWM into the transformer, and this will be limited by the time constant of the output filter choke, which should be only some milliseconds, fast enough to account for shaky hands for example.
Tim