The advice from Kutter is good. Keeping the original patina/old look is going to be the deciding factor on how serious you get with the rework. I have saved several barrels in about this condition by cutting barrel off just ahead of the drum threads. This involves a lot of planning and careful measuring.
Then make a new section similar to a store bought patent breech. Install the new breech in the newly threaded barrel and proceed as you would in building a new barrel assembly.
Yes, a lot of exacting math and planning. When doing this, you new to have a good reference point to work from. I have used the last barrel lug as a point to measure back from.
Done properly, your barrel pins or wedges should still fall back in to the original location.
Good luck,
DGB