With Factory Ammo a requirement, I would go with a 22-250, 243, or a 260.
I would also go a hair longer on the barrel to 15.75 on the MGM to keep the speed up for the extended Range you mentioned. (13 thru 15.75 is the same price on an MGM barrel)
You may also want to consider a Brake, especially if you are considering a Rifle Scope on your build.
Just my 2 cents.

Bob R