You have mentioned that you have to control current in 2-20 cycles. If you go by thyristor firing angle scheme it would be very diffult to achive control as you can apply correction in only 2-20 desceet step. For any feedback loop to work properly there should be large number of error sample & correction. Error sampling/correction is done at very high rate comapred to response time.(in most case like in case continous like in cas of SMPS) .
So if your welding ac cycle are from 2-20 you have design system for controlling current at 2 cycles you should be able to make correction in much shoter duration then 40 msec.
FOr this you have to go for a MOSFET or IGBT but your current range is two high. So you have to use connect a number of MOSFET of IBGT in parallel to achieve that high currect rating.