I'd want to try on a scrap set of barrels first, but I'll bet one could plug small screw holes in a bottom rib with a couple quick spots of MIG weld into the holes, quickly followed by a wet cloth or perhaps covering the solder joint with the heat absorbing compound sold by Brownells or Certanium. The key would be to localize the heat and contain it to a small spot and cool it before it could melt the solder. And you would sure want to hit the sides of the holes in the rib and not have the MIG wire travel through and arc on the barrels.
I'd buy the beer to watch how he did it. Given the size of the rib, I don't believe anything can be done to prevent the solder from melting when you put a 10,000F MIG arc less than a 1/8" from the solder joint. Removing the lower rib can be done in a few minutes without disturbing the upper rib or forend lug and short under rib. I've done that. Once off the barrels, welding the lower rib would be easy enough. Like I said, I'd buy the beer to watch how he did it.