Another term for Variac is the Autotransformer, on ebay I dont see many rated for 30A or more, so maybe there would be an issue making your own with a microwave transformer because the wires are thin. On my DIY tab welder I used welding grade cable, to get low output voltage and high current.
Another option is to use a generator when using the welder.
A transformer with 5 turns of 8 guage wire on the 110Vac input side of the transformer, and 4 turns output side would net you 132V (110V/5=22V+110V)
10awg can handle 30A, 8awg is 40A. That is totally doable with your average junked microwave transformer. I may have gotten my math wrong, but I'd say you can easily insert 8awg wire and loop it ~5 times, into both sides of the transformer. Just make sure that the directions of your loops stay the same.
You can view how to do it when you search youtube for MOT (Microwave Oven Transformer) tab welding. With mine I grounded the the unit, ground on the outlet to the lug on the transformer itself.