Farmer, did you have a chance to look at all the Pics from the link? Especially the pics of the Firing pin alignment, center or off center? The OP did a very good job with the Pics. I have owned 4 lcp's, (no longer shoot them). I did however check out the one I do own and the firing pin was perfectly aligned.
If it is correctly aligned then maybe a call to Hornady would be worth it. Some say their Ammo has hard primers. I know a pocket gun shooter that had problems with their training ammo and discovered big discrepancies with the Over all length in some of the ammo. I have a feeling in you case, it was the ammo and not the gun. I would call Hornady and report it. Ask if hard primer strikes have been reported.
In training ammo not such a big deal, but a Defense load is not acceptable.
By the way, you mentioned you shoot your LCP often but not your favorite. Might want to think about a Pico down the line. Very MILD shooter and a pocket gun that is fun to shoot. I enjoy shooting pocket guns and it is my favorite. JMO.