The biggest problem I have ever had with my LNL is the inner primer tube sliding out of the machined primer slide. It happened more often with a full tube than without one - my only guess is that the inertia of the ram going up and down combined with the little bit of friction from the primers inside would eventually work the tube up.
I ended up ordering a couple more primer bodies (the part that bolts to the press and holds the primer slide down, an extra large primer and an extra small primer tube and JB Welded the tubes into the primer bodies. When I change primers over, I simply un-bolt the primer body from the press and bolt a new one (with tube epoxied in) on. Works like a champ.
I also polished the chase where the primer slide rests, the underside of the primer slide and did the little chamfer job just like you did.
I haven't had a problem since then - clean the primer seat every 100 rounds (or however often I need to reload my primer tube) and rock and roll away.