I'm not absolutely certain about this, as I do not own the firearm. But, I feel I should mention a particular phenomenon I encountered with a SAA clone that belonged to a friend of mine a few years ago. It seemed to wiggle to the right, incidentally corresponding with the cylinder on the pistol. Now, I know the SAA doesn't have the Top-Break action of the Schofield, but bear with me.
The problem with the Colt turned out to be a cylinder indexing issue. Considering that the Schofield is exhibiting similar issues, but going in both directions, and that the cylinder on the Schofield can freely spin either way, I feel a little suspicious. Try loading some empty brass into your gun and closing the action. Next, cock the hammer repeatedly (Remember not to dry fire unless you've got snap-caps) to see if the cylinder can make a full revolution. If it doesn't, my theory would have a little more credence, and you might want to get on the phone with Uberti about getting a new gun. I certainly wouldn't fire it until someone knowledgeable said, "It's fine." or I at least discovered the source of the issue.