I'm aware that I should keep the scope as close to the bore as possible
True on a bolt gun, but the unique design of an AR requires the scope to be much higher from the barrel than you are likely accustomed to, in order for the scope to align easily with your eye when coming to shoulder.
As an example, if you attempt to install standard weaver scope rings on an AR, the extra high are not high enough unless you also use a rail or some method to get them higher.
The one piece mounts made by various makers such as Burris, Primary Arms, LeRue, etc are the best way to go. With such mounts the only thing you need to be concerned about is the diameter of the tube, not the height needed to clear the barrel with the objective bell.
