I think there's a good chance the brass could be the root cause here so I've already gotten some Remington brass on order, should be here middle of next week. You make a good point though, I may try my hand at lightly annealing some of the Starline case mouths just to see how that works as well.Ok I just wanted to confirm it was nothing basic.
I would also recommend paying attention to JE Custom. While I have done wildcatts and know more about the 6.8 AR15s than most he has likely done 10x case forming for every one I have done. i.e. he knows his stuff from everything I have seen him post on the forums over the yrs.
Honestly the issue you are having is minor. As he stated its likely hard brass at the case neck. You could switch brass going forward. As you already have what you have why not try a few seconds spinning the neck under a propane torch flame to fix it. You do not need to anneal it to ideal loading level just stress relieve the crystal slip joints in the brass structure of the necks. Its called the recovery phase of annealing. (IMO it likley what the low temp molten slat pot annealing kits are actually doing give temp and time vs typically foubd using torch or induction) Start out with a few seconds (3-4) in the flame spinning on a drill and go up or down in time till you find what allows you to finish the sizing.
Another suggestion for good brass is S&B its tough and might be hard but IMO to do this right no matter what annealing is in your future. In general its the closest I have found to my old early runs of SSA brass when Art Cox was still the owner. He was a great guy and super supportive and helping with testing etc donating ammo components piezo pressure test our barrels etc. Glad I had a large supply.
Another thing is if you turn the brass prior, then as you neck down, some of that neck becomes shoulder of the same thickness as the neck. That will reduce the likelihood of doughnuts forming as you have multiple loadings on it. You also will have less to finish turn and should make sixing down the necks easier with less snap back after coming out of the neck bushing.
The reason I asked if you had a barrel already chambered is you can do more to improve the case if you want.
But first what is your plan for this cartridge? What barrel length? What bullets are you planning? Paper punching varmint hunting what?
As your platform is ar-15 you are limited in COAL to 2.30 maybe another.01 but that's it with the roomiest mags unless you notch them. So the bullets you plan can play into what ideally you may want to change. Not to mention how much freebore you have cut.
The AR feeding angle has no issues with sharp 40° shoulders etc. Heck, it can feed short super fat sharp shouldered WSSM cases no issue which most bolt actions have a seriously hard time with. So lots you can do here if you are game and it fits your goals.
I did actually consider an even "wilder" cat, I ran across a cartridge called the 22 PDK which is a necked down and 30° improved 6.8 SPC case. It'll yield a hair more velocity than the 22x6.8 but requires custom dies and fire forming, so I decided not to go that route yet.