the zig zag winding is usually used for providing a ground connection to a floating delta system, that won't saturate the core when dc flows through it.
what might be happening is the SCR control of your welder is not zeroed perfectly and you are drawing some dc from the ac source. this is certainly a problem for my single phase AC welder when certain rods draw asymmetrical current.
but a three phase welder rectified to dc should draw very little or zero dc current, and a zig zag winding, i'll have to check the books again but i don't think it will do you any good.
what you might try doing is getting three, 100uF run caps connected across your generator (if wired for 240), this will suck up 30 amps of reactive current, pushing the voltage higher and canceling out the inductive load of the welder.
also you shouldn't have to switch between single phase and three phase, just wire it for center tapped delta. 120/240, and 240 delta. no wires to change, just a different outlet to plug into.