Greetings Vietnamcam,
My experience in working with low pressure loads is that the firing pin strike is enough to set the shoulder back enough result in slightly backed out primers. This would result in a shorter head to shoulder dimension on the case coming out of the chamber than when it went in. I think that your basic problem was a dud primer. I also think you are right in thinking that the projectile was jammed in the rifling due to the above and your minimal jump to the rifling. You may wish to seat the Game Kings a little deeper, at least for the first load. I use 1mm or .040" as a start jump and have seldom needed to change it. The deeper seating would prevent getting a repeat of your problem.
Regards Grandpamac.
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