The answer is that until you isolate the specific variable(s) causing the higher-than-expected ES/SD, you won't really know how to lower them. There can be quite a number of reasons you might observe that kind of velocity variance, which I would call excessive, but not necessarily "severe". That list might include but not be limited to (ranging from most to least likely): neck tension (interference fit) variance, excessive or too light neck tension, sub-optimal primer choice for that particular load, charge weight variance.
I'd start by making sure you anneal every firing, and being certain your re-sizing step is producing consistent neck tension, as well as the proper amount of neck tension. That means measuring the diameter of case necks just below the mouth before and after bullet seating. You want to see a difference (interference fit) between the two measurements of somewhere in the neighborhood of .002", which typically means above ~.001" and below ~.003". You can easily test what your rifle prefers and how it affects ES/SD by using bushings to size a few cases each that give you very close to .001", .002", and .003" neck tension. If your neck tension is below .001" or greater than .005", you might see an improvement by bring it closer to around .002", although this number is not written in stone. The second aspect of neck tension is that you want it to be uniform, regardless of the actual value. That may mean using a specific diameter mandrel to open up the necks to the desired value as the final sizing step after re-sizing cases with your sizing die. You may find it necessary to turn the necks and make the neck wall thickness more uniform.
Sometimes, switching primers and re-working the load is all it takes to see a noticeable improvement in velocity variance. If you have another type of primer you can try, or if a shooting friend does, you might load a few rounds side-by-side with the two different primers and see if one makes a noticeable difference.
As I'm sure you noticed, charge weight variance is the last of the short list I mentioned. Although some shooters striving for the utmost precision will often weigh powder to an accuracy of +/- half a kernel, that is not usually the reason for excessive ES/SD. In fact, you can easily make a rough calculation of the theoretical effect of charge weight variance by dividing the maximum charge weight variance by the total charge weight, then multiplying that number by your average velocity. For example, altering charge weight by 0.1 gr in a typical .308 Win load with a Berger 200 gr bullet over Varget will typically change the measured [actual] average velocity by somewhere between 5 and 10 fps. In my F-TR setups, 43.5 gr of a typical Lot of Varget in such a load gives almost spot on 2650 fps from a 30" barrel. So, 0.1 gr/43.5 gr = 0.0023. If I multiply 2650 fps by 0.0023, I get 6.1 fps expected velocity change for one tenth grain change in powder weight, which is well within the actual measured range. If one tenth grain of powder changes velocity by only 5 to 10 fps in a .308 Win case, then the charge weight would have to vary by as much as 0.4 gr between loaded rounds to produce an ES of 40 fps, assuming charge weight variance was the sole cause of velocity variance (which it probably isn't). In other words, charge weight variance can certainly cause velocity variance, but it would take a fair bit of charge weight variance to account for more than a few fps in terms of ES/SD. One way to test this would be to throw a few charges with your Chargemaster, then weigh them on a [separate] accurate balance to estimate how precisely your Chargemaster is actually throwing charges. I rather suspect it is not going to be off by several tenths of a grain, but again, it is easy to determine that empirically by double weighing thrown charges so you know for sure.
Excessive ES/SD can sometimes be a very challenging issue to decipher so that you can correctly identify the cause and address it. IMO the best approach is a stepwise analysis of your brass prep as outlined above, trying a different primer, and checking your powder weighing apparatus. It may seem painful, but it's not really as bad as it might seem. Annealing cases, as well as checking each case prep for proper sizing and neck tension (interference fit) is something I do with at least 10 cases from every single prep I do. That way I know what I'm working with, and it makes it much easier to troubleshoot if something is off. Once you've done that a few times, it will become the "new normal" in your case prep routine and not seem like any extra effort at all. That same is true for whatever you might need to do to address or fix any specific problems you might find are likely to be causing excessive ES/SD. Checking the accuracy of your balance from time to time is always a good idea, even if it seems to be performing flawlessly. In any event, best of luck solving it!
