this thread being reposted finally motivated me to go to the garage and install the one I had purchased several months ago.
the spacer has one end that is beveled, this matches the bevel on the shoulder.
Install went pretty easy assuming you have a pair of relatively thin 19mm wrenches. However, the Surefire manual did not correctly list the Aug thread pitch as left hand. Fortunately after having no luck and slipping a wrench once, I decided to go upstairs to double check on the PC and found out that it is indeed LH pitch. After that, barrel in vice, had one wrench locked against edge of work bench and gave the other one a good amount of torque and it broke loose. Looks like loctite so some heat wouldn't have hurt.
The surefire hider doesn't look out of place on the Aug although the tulip hider did look better.