First, I'd try to figure out why it broke - because a repair is rarely stronger than the original and whatever broke the old will brake the new that much faster.
mig would be my very last option, it typically has very little penetration and very little strength. It is the weld of sheet metal and not that of structural and machine components.
Lugs are glued on by the usual methods of silver solder and brazing. Those methods would be in my first train of thoughts, way before anything electric.
Don't think about saving short term time, think about safety first and make it last.
Best of luck.
