I had the same problem with my Lyman hand primer. Issue was not using Lyman shell holders as they are thinner and allow the press to push the primer right into the pocket as intended. I was using hornady shell holders that are thicker and were restricting the range of motion. They Lyman tool only has limited travel so you can’t over seat the primers, it just runs out of travel in your hand. Failing that, I would gives the pockets a small ream.
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