Sounds like it needs a proper fix, not a quick fix. Unfortunately the cure probably isn’t going to be as simple as a bend this, tighten this pin or add a shim here, etc.
As strong as a Jones underlever action is, they do get loose. Sounds to me like you’re going to have to build up the cams on the underlever and make sure that there is adequate bite between the cams (bolt) and the barrel lumps.
Some jones underlevers were snap actions, aka there’s a spring in the action that keeps the lever in place, most of the medium to lower grade actions relied entirely on friction between the cams/bolts and the barrels lumps. It should not be a difficult fix to get the mating surfaces to bite. A little laser welding and some good fitting and it’ll be ready for the next 100+ years of service.