Hey Ben sorry I assumed you were doing the full precision craziness in loading loading so lets drill back for aa second. And if any of this is stuff you know please disregard just trying to be complete here.
Re: Your chain
The biggest q from me is are you using a bushings to size you necks and then a mandrel to set neck tension? … If you are not setting neck tension to something like .002" Id say look there first. I assume you understand that process if not and for any others reading .
A standard FL sizing die has a de-caping stem with a ball on it that on the stroke of the die closes down the big fired hole and then opens It up the neck to accommodate the seating of the bullet with some grab or bite ----neck tension.
The next step down the rabbit hole is to use a bushing and a mandrel to accomplish this. The bushing acts in the sizing die as the device that resizes the neck for your fired state of completely open. They are precision collets that are measure typically to the thou and chosen based on the sixe of a loaded cart outside neck diameter.
The neck tension is then set to the desired size usually from .001 up for your desired effect. This is also chosen based on your components and the final neck diameter size of a seated bullet . .001 is really loose and typically for single feed bench rest for example. The looser It is the easier the bullet escapes. When you do this sizing there is some spring back of the brass due to memory this will change depending on how many firings/ sizings and state of the brass with or without annealing. Point being with the Bushing and mandrel you can really create tighter tolerances and consistency on your brass and what force It takes to seat Consequently, the variances in how hard It is for the bullet to escape the case. The harder It is the more pressure builds behind the bullet . More pressure is a change in velocity. This could look like a flyer.
So if you are not doing this It would be my first look… there are many ways to do It I use an SAC Modular sizing die which does all of this in one stroke decap/ FL size and mandrel instead of the way I did before in 3 steps. saves a ton of time but they are like $400 (Slap my ass and call me sally)
PMA and others make mandrel dies that are inexpensive relatively and the carbide mandrels are not cheep but you will see a huge diff. You could use something like a LE Wilson Sizing die that takes bushings. If you do buy SAC bushings fit and they are awesome . LE wilsons own bushings are great and if you are making Hunting ammo which It seems you are got with that save a couple of bucks…
Wind up Neck tension is the biggest spot in the chain to lower SD/ES if you are not concentrating on that today
Now to the arbor press The K&M, see below, I mentioned, there are others, is non camming press with a small handle in which you use an inline seating die . this die really holds the components in a tight tolerance centers and seats the bullet perfectly strait with the least amount of run out. Another rabbit hole. Now this press has the option of adding a power pack which measures seating force, this is what I was discussing, see the Dial on the top. You can with the low pressure pack see the seating force down to the half pound if you really pay attn. Now for the 7mm you might want the larger force wich has less precision and shows much higher seating forces I’m not sure…the bigger issue is your tactile control and sensitivity to what It takes to seat a bullet. With this set up really fine. With your Redding you really don’t feel the bullet seat at all. The difference seat to seat is huge and you get a real sense of the differences cartridge to cartridge. Now if you can see It and feel It you can sort for It and that flyer will most likely disappear.
Disclaimer, that doesn’t stop my Yips or errant shots. I make plenty and with SD’s in the 4 range or lower It ain’t the cart and I can take that out of the equation.