The LNL press is unique (and- it's one thing that really sets them apart from Blue) in that it uses half-indexing.
One pawl adjusts indexing for the upstroke, the other for the downstroke.
If it's dropping into the detents, it's indexing properly.
The new EZ-ject system is supposed to work...but mine often hangs up as well.
That is the one "complaint" I have...but I really don't care. I just pop out the finished round, while I'm putting in the next empty brass and placing the bullet.
Do you have any other calibers that you load for?
I can't help but wonder if you might somehow have a defective shellplate that's not aligning the case correctly.
Your common theme- including the primers not seating- screams of misalignment, but from what you say, the press seems to be indexing correctly.
If you're self-indexing the press, and tearing up cases as you say, it would have to be the dies/shellplate- or the press itself, meaning the upper stations are somehow out of spec/alignment with the lower plate.
I took a look at mine...and have a "theory"...if it's not your dies or shellplate.
If the lower plate with the detents is not perfectly located, you can be indexing correctly- meaning the shellplate rotates and drops into the detents- but still be out of alignment with the upper stations.
If that were the case, you would have a manufacturing/alignment issue, NOT an indexing issue. You would be consistently "off" by the same amount, at every station.
Hate to say make another call to Hornady, but if that makes sense to you, run it by them and ask if they've had that happen before. If so, only solution is a replacement press.