Damaged muzzles usually just open the group, not shoot to one particular spot, I think.
Some 'shooters' regulated their own doubles by filing the muzzles on the sides, tops, bottoms or all three to get a particular load to shoot together. Filing on the outside 1/2 of the tubes would make the balls shoot more towards the centre, while filing on the top would make a barrel print lower, bottom to print higher, centre 1/2 to make it shood wider. This was evident on some original American made doubles as made by Colt. I domn't know if any Reed double sexist that have this 'filed-in' characteristic.
Another type of 'damage' is to 'oval' the bore, something that is fairly easily done to a thin barrel at the muzzle. An oval bore will probalby dably 'burn' or 'shred' the patch as the ball leaves. A slight oval top, bottom of sides may have th same effect as 'filing' and therefore cause the stringing shots. Different holds on the rifle, of course, will have the same effect.
Fix one thing at a time. First of all make your holds identical. I'd probably 'fix' the bad trigger, though, to get them closer to the same pull. It is the second barrel that 'should' be harder to pull, not the first, which is usually the right barrel. Elmer keith,on the other hand, preferred to shoot the left barrel first, letting the recoil shove his hand further up on the wrist to grab the front trigger for the second shot. He had small hands, whereas my meat hook hands don't need the recoil's help to change triggers. I fire the front trigger first.
I suggest that if the left trigger is good, as in it doesn't fire if both are cocked and the front is pulled, then repair the front trigger's sear engagement to the same pull or slightly less and then always fire the front trigger first. The beauty of the double is to be able to fire quickly, a right and left (left if needed). You can't do that if both aren't cocked. If the gun 'doubles' when one of the triggers is pulled then the triggers need repair (angle of the engagement). This is why the right trigger is usually lighter than the left. It is usually fired first, therefore can have a lighter pull for better accuracy.