I would say to do just as Keith O said, but I would weld the backing plate on rather than epoxy.
You definitely wouldn't want to stick weld, as you would most likely warp or burn though the CP. You could do it very easily with a small mig or wire-feed. I've done such repairs with my Millermatic and they've turned out just fine. I use a flux core wire, so I still need to mindful of the heat, but I typically use a very low setting as it isn't really necessary to get a full penetration weld for this kind of repair. If you mig weld with a bottle (CO2, Argon, mixed, etc...), you can weld as thin as 22ga. sheet without burn through or warping.