Concentricity Concerns

It is indeed "trash" Lake City brass. However it is 100% consistent from piece to piece, manufacturer to manufacturer, they all cant in the same exact way. Yes it appears in the photo to align with the post behind it, and even if that is true then that should mean that my die or die holder is out of spec.
I don't know if this will help. But one reason I upgraded my Lee single stage press was. The bearings on the ram will
wear out and allow the ram to move left to right, back and forth. Also if there is any flex in the mounting of the press
(movement/slop) this will add up every time you lower and raise the ram. ( Just one more thing to check.)
I normally check the base for squareness with my Neco gauge on my 5.56/223 cases. As a rule of thumb, the cases that I shoot in my autos, I do not shoot in my bolt guns. I hope this helps, but it could be a number of things.
Please share what you find out.
 
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1) Rotate the case in the shell holder with the press just as it is in the picture and observe the case mouth does it move?
2) Rotate the shell holder with case in it just as in the picture does the case mouth move?
If the case mouth in #1 moves it is the case heads being off from firing. If the case head in #2 moves it is a crooked shell holder. If the case head don't move it is a press alignment problem.
 
There is definitely play in the shell holder if you rock it back and forth, and I do have a second shell holder that I tried but I get the same exact results ... both are Lee shell holders. Measuring the run out on the case neck also interests me the most, and I'm looking at the Sinclair concentricity gauge (suggestions on other brands?) but if I bought that now and confirm the run out is awful, I'll have to save up to add a new single stage press to my bench. I'm thinking I should just bite the bullet on the concentricity gauge now because it's something I should probably have on my bench anyway.
I use the Neco concentricity, wall thickness & run out gauge. This gauge does every thing with precision. If its good enough the the ammo manufactures and the US military, Its good enough for me. (just kidding about good enough for me.) LOL The gauge is a Gem .0005 and has V-Blocks. I was looking at the Sinclair and 2 other higher price tools
that do a great job. But the Neco does it all, and it does it right. Just my 2 cents and what I use.
 

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Looks like the shell holder slot is too deep, it looks to me like the case doesn't line up at the center of your die. When u move the brass up to the die does it go in straight or of to one side? If it doesn't go in the center of your die you need a new shell holder. If a RCBS shell holder won't fix your problem, get the rock chucker press to go with it.
 
Bottom line? How's the ammo shoot and how much accuracy do you expect from your platform? If its 1.5 MOA rifle that won't hurt at all. If you're shooting a 6br for bug holes I'd get a new press. Have to add...my brass on my Rock Chuck Bullet Swage hits the edge of the Hornady dies for my 6.5 Grendel all the time. I generally rest my thumb against the case to get it in straight. It still shoots pretty good.
 

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I will say from experience the RCBS summit press and RCBS case master concentricity gauge both are excellent tools to produce concentric ammo. But for that matter the Hornady concentricity tool, Forster benchrest dies and seater, and Lee collet neck dies are also proven winner's as well. I used everyone of these items today working up a bunch of loads in several calibers. Hope you get things figured out 🤔
 
That was a good question and something I hadn't considered since the press has been mounted in the same spot for a few years. It's not perfect but it's pretty dang close, best I could measure was about .02 off and it is in the direction the cases lean, but I can't imagine that small of level issue is causing that much lean in the case. I played around with the shell holder some more and it has a fairly significant about of play in it ... not sure if that's by design or not?
MY old Orange Crusher was off plumb , but I didn't know it. Kept having trouble with the deprime pin missing the flash hole. It looked like it lined up fine. The bench is level and sturdy. So for the halibut, I put a small bubble level across the top of the ram , one of those line levels. It showed high on the left . Not much, bubble was only about 3/64" off. I shimmed under the right side of the press base with pieces of an old broken hack saw blade that was handy. Bubble level on top of the ram then showed center/plumb. Fixed the deprime pin problem . That was over 10 years ago. I planned on putting a proper shim plate in place but it slipped my mind until this post of yours.
 
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