Howdy Again
Another thing I forgot to mention is that I always use a Gravity Assist Device with large primers in my Hornady press. I use a brass rod from the hobby shop. 3/16" diameter, cut about 19" long. I used a Sharpie to make a mark on the rod indicating when the primer tube is empty.
After I drop all the primers into the primer tube assembly, I add the Gravity Assist Device. I run it right down the primer refill tube, it will drive out any primers that got stuck in the plastic part at the end of the filler tubes. Be very careful if you use a Gravity Assist Device and do not drop it on the column of primers in the tube, gently lower it. Then lift the primer refill tube straight up and off the Gravity Assist Device.
Sometimes there is just enough gridue in the primer tube assembly to impede the primers flowing smoothly. Or maybe one is a teeny bit oversized. Whatever the case, the Gravity Assist Device will keep primers flowing down in the tube.
Also, be sure the spring loaded thingy that pushes the primers up into the primer pocket from below is screwed up tight into the base of the press. It tends to loosen over time. And be sure to take it apart and clean it every once in a while. Primer dust can build up inside it and prevent it from retracting completely. This can cause the primer shuttle to hang up when it tries to return with a primer. Be sure to have a few extra spring clips on hand for the spring loaded thingy. They are tiny and real easy to lose. Trust me on this.
Stupid question time since I'm not familiar w/ the LnL priming system: is there a chance you can take a couple of thousandths or so off the bottom of the tube and avoid both shimming and having to loosen the screw?
Not really. The inner primer tube in the assembly sits in a diecast base. To provide more clearance the base would have to be raised. Shaving off the bottom of the base would lower the inner tube. Part of the problem with this design is that in order to change between large primers and small primers, the inner tubes have to be interchangeable. That means the the tubes are a slip fit. It also means they can inadvertently shift up or down a little bit. If they shift down just a tiny bit, they can be in the way when the shuttle tries to slide past. If they shift up, primers can get caught in the loose space that has been created. I have messed around quite a bit getting the tubes to be a tighter fit. It usually involves wrapping some scotch tape around the bottom of the tube to keep it in place. This solution usually does not work too well.
I have some other ideas and will probably try them out fairly soon as I am way far behind in loading up all my cowboy ammo for this season. If I have any earthshaking breakthroughs, I will report them here.