A mushroomed hammer face in usually not a problem. I'd check the firing pin protrusion when it fires. Sounds like the right one is slightly worn. Measure it against the left one. I've seen the firing pins worn or distorted on both ends. Crescents weren't made with the best materials and soft metal wears over time. Replacing a firing pin is an easy option to see if your problem goes away. If cheap just swap them and see if your problem moves to the left barrel.
Another thing to look at is rim cut depth on the right barrel. I've seen a few which were "cleaned up" by some "gunsmith" when they cleaned up a rusted chamber and some shells seated too deep. Longer firing pin fixed the problem in that case or just different brands of shells.
