here is my .05 (remember, no more pennies). With the improvement of quality ammunition over the years, the need for checking thickness on match grade ammunition has become an exercise in futility. Is there still a thickness difference, yes. Is it substantial enough to make a differnece? in my opinion and the opinion of article writers and others more knowlegeable than me, no. And these are people who shoot benchrest seriously.
Not buying match ammo you say? Then there is a bigger difference in rim thickness, but you are using guns of lesser quality and all the sorting in the world is not going to allow you to shoot needle heads at 50m.
I used to sort my ammo then gave it up for the above reason. I even used to sort by thickness and then resort after I weighed each round (that was a lot of work). I saw no difference.
With all this being said. shooting is as you know a mental game. So if you think sorting your ammo will produce better results, then it will. BTY I have a homemade gauge that I can sell you for $20 shipped but I suspect I will have it till I die.
Paul