I've had my LM since '95, before all the bad press on the web, and before all the videos. I just read the limited instructions and started reloading.
I had about 7,000 rounds thru it before I had to replace the primer slider that came with the machine. And the only reason I had to replace that part, was I started running range brass and found out about crimped primers and mangled extraction grooves.
Before the range brass, I bought a box of ammo, shot that at my backyard range, and picked up the brass to run in the LM. NO crimped primers, my guns weren't worn out and didn't damage the brass. So I didn't have any of the priming issues I read about on the web; like yours.
When I did run the range brass, I got all the problems you describe. Did some research on the web and found all about crimped primers. Now all the range brass is deprimed and primer pockets reamed. I use a small 3/8" countersink in a cordless drill. EVERYTHING gets reamed. All you need is one crimped pocket to have the primer slider get trashed. The primer doesn't install in the pocket, so it's floating around down there waiting for the next primer to come along. You've been taking that apart and know there's only room for one primer at a time in there.
Once I went to the prepped brass, no more primer issues. I had to use the Auto-Prime hand tool waiting for the new sliders, now I use the LM to resize a deprimed, reamed case, then use the LM to insert the primers. Did about 500 .223 cases like that last week. Not one messed up primer with that reamed brass.
If you have some brass that you shot and picked up, try running that in the LM. Nothing that has crimped primers, nice clean, commercial stuff. I'm reading the cops are using stuff with crimped primers, just like the military. So even buying stuff off the shelf at Cabela's might not be safe....
So, are you reloading stuff you shot, or range pickup? Big difference in how it runs in a LM.