You may find that the process variable (ie weld current) varies slowly (due to wear, metal thickness etc) in which case you only need to occaisionally correct the weld current. If you know the transfer function of your output control, you can add/subtract a 'fudge' factor if your current measurement is outside a window. You might only need to do a correction once per weld. Therefore I don't see a problem in using phase control for your welding. As for varying the frequency - unless you increase the frequency substancially and build a VERY high power inverter, I don't think you'll get much of a gain.

On another note, my little inverter welder works much better than my old tranformer type. The arc is much smoother since it is rectified 10khz! Whilst it's good for 200amps, building a 20,000 amp one is a little outside my league! The ferrite core would be fairly large methinks!

Also, since you use two phases of a 3 phase feed does not make your system bi-phase! Your transformer sees one sine wave at the phase-phase voltage.