As I said, I am unfamiliar with Colt doubles, so I do not know if you could simply turn the hinge pin to move it around to an unworn section, or if you would have to replace it because it only indexes properly at one point. It appears the head is curved to match the curvature of the action bar. But if it is off face, it could likely be removed and welded to build up the worn area. Even if you could turn it, I'd assume there would still be wear in the hook as well. But if a thin shim on the water table makes things tight, it could be that your wear is in the bolting surfaces, even though there appears to be a gap between the barrels and standing breech. Again, hard to tell from this distance.
I think a Colt factory letter is going to be nothing more than a $100.00 expense to tell you that your gun probably came from the factory with 30" or 32" barrels, and has been cut. This is why it is never a good idea to cut down a perfectly good vintage double to make a Cowboy Action Shooter. It absolutely kills the value, and unfortunately, there are already a lot of them out there that are already shortened, if you take the time to look.
