I've thought at length the last two days about this thread, and I've typed a reply here 4 times now - ultimately ending up with a lengthy explication of why the process described by the OP just doesn't hold water, and I've ended up with ridiculous walls of text which I fear will miss the mark as important points could be glazed over when piled collectively together.

I hope no part of this comes off as insulting or condescending, but I know when I type for brevity, it almost assuredly takes on that tone. I'm empathetic enough to acknowledge that shortcoming, but I'm sociopathic enough to continue to speak/type as I naturally would. This is going to be long, but I assure you, it could be much longer to explain these principles.

I'm happy to recreate the (very wordy) responses I penned in my first drafts of this response if there is interest from the OP or others, but the punchlines are as follows...

I'm a professional technologist. I spent the first half of my career as an engineer, developing technologies, products, and production processes, and now I'm the guy who guides engineers to develop reliable and responsible processes and products. I came to this career path because it's who I am and how I see the world. So I can't help but look at EVERYTHING I do through the same lens. I'm not saying anyone should be conducting high level statistical analytics on their reloading data, but without question, there are fundamental principles of Lean Manufacturing and Six Sigma methodologies which would help this OP understand the error in their processes.

First and foremost, when developing any process, you have to define your "problem" to be solved. "Fix the problem, Fix the process." The "problem" we're trying to solve in reloading rifle ammunition for precision is group size. Specifically, a "fix" is something which measurably and reliably reduces group size. You have to define the problem to define the process, and many, many guys get caught up in trying to fix the wrong problem.

In that light - sorting by weight is a fool's errand. Been there, done that. I've done the data analysis myself, and read the same work done by others at high levels of statistical validity. The OP has said it above - the collective "we" of precision reloaders know that increased consistency in case VOLUME has been proven to have a measurable reduction in group size. However, readily available data has proven case WEIGHT is not a corollary for case VOLUME, such you might actually be INCREASING your inconsistency in case volume between your cases because you are sorting by weight. Just stop. Period. It's a long debunked process, and you're not doing yourself any favors by continuing to do it.

Equally, weight sorting cases does nothing to "fix the process." You misidentify the "problem" by thinking inconsistent case weight is a problem, but you do nothing to actually FIX the problem by culling the cases. You are, however, increasing waste, and increasing the cost of your finished product batch. The effort you spend in weight sorting cases would be better spent by VOLUME sorting cases, and the money you lose in culled cases would have been better spent by purchasing better quality brass from the beginning which had lower variance in case VOLUME. So again, weight sorting cases is a fools errand. Just stop.

Hand sorting cases with a mandrel pin and a neck bushing is another misguided process step. Again, I'm certain you feel as though you're significantly reducing variability in your cases, which HAS to be good for group size, right? Not really. Again, you're reducing the value of your brass by adding ANOTHER waste generation step - you could have bought better quality brass from the beginning, or done ONE simple step ONE time to actually FIX THE PROBLEM and reduce variance, instead of simply using quality control methods to reduce variance and create waste. You could also spend the same time (less, in my experience), by simply sizing and expanding with those same tools, actually promoting consistency among the batch, instead of creating waste.

The mantra I teach to young engineers to describe this is, "spend money where money gets made." Which in this case, the first "money" is your labor time, and the second "money" is the reduction in waste. If you neck turn ONE TIME, then bushing size and mandrel expand all subsequent firings, you would have 100% yield in that sorting step, and have the same level of time invested (likely less) to create a greater value product. Your sorting step might arbitrarily create culls at every firing, whereas it really doesn't add any value to your brass.

In the same stroke, @bronco22000's question to me is apt - he observed that when he crimps with a Lee collet crimp die at the end of his process, his group sizes shrink - which if the world were an onion only one layer deep, sure looks like it is a "fix" to our "problem" (reminding here - our problem we're trying to fix is excessive group size).

However...

From where I sit, and knowing what I know from reloading precision rifle ammunition and principles of production process troubleshooting, the fact the Lee Collet Crimp die reduced group size is an indicator of a broken process step somewhere prior to crimping. The function of the collet die is simple - it's NOT creating neck tension, it's just deforming the bullet slightly to create a physical barrier which must be bent out of the way to allow the bullet shank below to exit. So, why does it reduce group size? It can really be only one of a few things, or combination therewithin - it could be improving concentricity, which would mean there's something out of spec in the rest of the process, either runout in the press ram, eccentricity in the sizing die, or eccentricity in the rifle chamber. Since it happened over multiple calibers for Bronco, it can't be an out of spec sizing die or out of spec rifle chamber. MIGHT be slop in the press ram. BUT... it also might be improved consistency in primary ignition due to increased resistance to the bullet moving. This could be an indicator of a few things - insufficient neck tension, which would mean the necks were too thin, the expanding spindle too large, the brass too hard, or the sizer neck too large, OR, inappropriate charge weight or powder choice. My money would be on the latter. By adding a bit of "back pressure" to the primary ignition, you're creating a more consistent pressure ramp at the front end of the curve. Again - to fly the same, the bullet needs to exit the barrel at the same relative harmonic position. If your powder charge isn't in the node, it will be extremely sensitive to variability in bullet weight, bullet diameter, neck tension, powder composition variation, charge weight variability, case volume variability, primer brissance variability, etc. By "boosting" the primary ignition, he's likely improving the consistency of the secondary combustion pressure curve from one shot to the next.

So on MY bench - if I saw that result on target, I wouldn't be adding a crimping step, I'd be going back to my gear and to my process to troubleshoot. I'll "fix the part where the part gets broken." If I have eccentric necks due to an obloid expander, I'll replace the expander. If it's because of a sloppy press ram, I replace the press. If it's because my powder charge isn't in the node (most likely), then I fix my charge weight target or powder selection. When it cycles back, the crimping step should have little to no improvement, and by all rights, SHOULD actually create a problem, because "every step we take is a mistake we make," a recognition of the inherent error induced by every production step. The fact it reduced group size would tell me I did SOMETHING wrong before that to increase my group size - and my experience would say to look at my powder charges.

Hopefully that's clear, and again, hopefully it doesn't come off more boorishly than I intended. I'm happy to elaborate further on any of these aspects, but the forum capped me on my character count on the first two drafts, so I scrapped it and started over to help keep a focus on the critical points.

But for the OP - ditch the hand sorting with the bushings, ditch the weight sorting. Look up Newberry OCW, Satterlee Velocity, and Audette Ladder tests, ask some questions about appropriate bullet jumps for your desired bullets, neck turn if you need to, and shoot smaller groups than you're shooting today.