Your rim cuts are too deep, at least for the rims on thise Winchester AA H....S... shells. Briley and likely others can install steel rings and recut the rimcuts shallower. I'm sure that would not be cheap. If using other primers takes care of it, that's surely the way I would go, too. I had a cheap, American made .410 that was the same way. I got it to quit by adjusting the hammers to cock a tiny bit sooner. The gun wasn't worth what remodeling the rimcuts would have cost. It was a something Empire Grade, as I recall.
