Use 1/4" mild steel bar, whatever width you wish to do the extension:
Tack it in place, check that it is square and true before welding:
Stick welder will do, this is 1/4" mild steel to 1/4" mild steel.
Barely visible in this picture (that is mostly about my home-made axle wrenches) is this extended swingarm. You can see the horizontal plate added for side to side stiffness. Total weight? 1 lb over stock. Total cost? under $10