Time for some "hard love". It looks to me like the hooked breech and tang do not match the size of the barrel, and all of the metal of the standing breech tang has been filed away from one side. I've used dozens of these L & R sets without incident, so don't blame L & R. On the last Hawken rifle I built, I used a breech and tang I bought at Dixon's Fayre - make unknown - but when the tang was fit to the hook, and the plug in the barrel, the tang scooted off to one side a bit. If I had inlet it like that, it would have been very noticeable. So I bent it cold using Ken Guy's system of three rods in the vise, clamping the tang gently between the rods and applying pressure to bend the tang straight. Easiest thing to do. Then, with the tang on the hook and the barrel upsidedown, looking down the middle flat, I could see that the tang was dead centre. I soft soldered the tang to the plug, and inlet the unit right down the drawn centre line. All this is just to illustrate that parts can not be assumed to be perfect and may need a little judicial work to make them so.
Now, back to your dilemma. I cannot see how you can save it. Both the tang and the wood are beyond rectification, in my view. Too much wood has been cut away from the lock side. Unless you are willing to set new wood into the tang recess, and glue more maple to the lock panel, I'd say you will want a new stock blank.
Dan Pharis' advice on set up is right on.