Why not do a lap weld with another layer of material? Is clearance a problem?
Tack weld another piece of material (fairly thick sheet steel or thin flat stock) on one side or the other (hammer it straight), then a piece of filler for the middle. You can actually use steel rod for this or a long bolt (built in bezel). Short welds (passes) no more than 3/8"-1/2" at a time. One end, then the other, one side then the other, check for straight (maybe use a vice) let it cool down between passes.
Grind off the backing material and repeat with the other side.
Depending on function, maybe heat it up red, hammer it straight and dump it in a pot of used oil. Or let it lay on the garage floor until cool.
You have to take function into consideration, just how strong does it have to be. If it cracks and fails, will it be catastrophic?
One bad thing about MIG, is the welds are universally fairly hard and when they are harder than the surrounding material, things can stress in strange ways.
My MIG welds rarely (never) fail, if it does crack, it is often where the weld meets the original material, right at the edge. Weld failures are most always from vibration or expansion and contraction. The only exception being is if you dump your work into water when hot, it may crack most anyplace and stresses the work in odd ways.