I have a couple of the Hornady lnl presses and use them for all my reloading, but have heard of people having certain problems with progressive presses when full length resizing. Have you done the 308 reloading on the same press? If so maybe try another press. If that’s out the window then it’s about the dies. I just checked what 308 dies I have been using and they are the Redding premium die set and a lee crimp die. Not cheap, but they give more precise bullet seating and have given me good sizing every time. I use a Lyman case gauge block set when checking my loaded ammo since they are cut to minimum sammi specs. If they fit they chamber for me.
Good luck