Having had experience in making tumblers for sidelock shotguns through the years, and having made another tumbler for a side lock double rifle just last week, I say that welding a tumbler especially welding one that has broken in the unfortunate place as this one, is not good gunmaking practice. Hardening two different alloy steels to the same hardness and toughness(the base metal and the filler metal) in this case for this tumbler will be like buying a pig in a poke. Of course this is only my opinion, and my answer to the original request of what to do. This is a job for someone who knows what he is doing and about such as Dewey Vicnair.
eYe...as any competent gunsmith will tell you.
