First question:Is this rifle a purely factory built Armalite product that you have not modified/changed?(edit:OOPS! You answered that in your post!)
This will tell us if we need to study what was changed.I won't say any company never has a non-conforming product escape...But if it is as Armalite made it,the likelihood the rifle is wrong is very small.
You make no mention of what ammunition you are using.
Are you using factory ammo with near 7.62 Nato spec length and bullet ogive?
What I am getting at,might the rifling be contacting the bullet?
Are you shooting handloads?A number of possibilities,at the top of the list would be not quite understanding that seating dies also crimp.Bumping your seating die on the shellholder will collapse the shoulder a bit,causing the case diameter to enlarge at the shoulder.
Necks may need trimming? Cartridge headspace too long?
Ejector plunger not moving freely?This can be caused by loading hot.Brassslightly extrudes to the ejector hole.A crescent shaped brass sliver is sheared as the bolt rotates.It crawls in between the ejector and the bolt.If your ejector is not free,it can block going to battery.
Some "NATO" surplusammo is surplus because its out of spec on the hot side.We had some Portugese battle pak ammo like that.Chrono'd 2900 plus.It would stick in the AR-10 chamber,FTE.It ran fine in the FAL.Point,even "factory" surplussed ammo could have an issue.And,it could cause the sticky ejector.
A Dillon or Wilson chamber type cartridge case gage,at about $25 may tell you there is an ammo problem if the gage does not accept the ammo.
I do not know if this next idea could have anything to do with it,but early AR-10 used a modified M-14 magazine.At least an option now,Armalite offers the AR-10 that uses M-110/DPMS/SR-25 type magazines.I do not know if you could even seat the wrong magazine,but if you could,that might cause a problem.
In any case,Armalite makes a fine rifle,and Believe they would give you support.
To carefully observe and solve this problem without shooting is a good idea.The rifle needs to reliably lock fully in battery.Just a little bit not quite locked up is not a happy situation.
It almost sounds like you may be describing "short stroking".The bolt is not coming far enough to the rear for cartridge pickup?
Is it brand new?Sometimes with new parts there is a little leakage at the gas block.After a little shooting,fouling self seals it.If you have moved the gas block,the alignment of the bbl port and the gas block port may be disturbed.
Also,there is a wide variety of 308 sporting and mil type ammo available.A semi-auto has to have certain pressure parameters within arrange to operate.Your AR-10 may have certain ammo it just does not like.Initially,try some near Mil Spec ammo to see if it runs.Maybe Black Hills 168 gr match or so.See how that goes.
While there is some flexibility in tuning AR type rifles with springs and buffers,etc,I would NOT start there.I'd try changing ammo first.