Chuck, I think you bring up a good point. I saw your pictures of the barrels you sleeved and of the cracking. I do believe that if the barrels have enough carbon in them, then these outer edges will harden because of said carbon content. Unfortunately, the only way to find out is to weld them since we do not have any idea what these barrels are made of.
I know some steels are better if they are heated before welding.

David