Before you order anything, go to this site, and talk to them.
http://www.accuracysystemsinc.com/index.php
This guy will also make any semi auto shoot. My first center fire in 1980 was a Rem 742 semi-auto chambered in 30-06. I was lucky to get a 5" group out of it at 100 yds. At the time I was coming out of the military, and my opinion of semi auto's was really poor. I started reloading at the time because "those that know all" said I could tune the gun with some reloads. I got it down to a 3" group, but thats not good enough. Prior to that I had LOTS of experience with the M-16A1. It really sucked to have to stop in the middle of a fire fight to clear a jam and clean it so it would shoot again.

Things have certainly changed now. ;D If you have one of these guns, and desire to make them accurate, go to that web site and read the testomonials. He doesn't advertise this,(I don't know why, but learned this from a long distance shooter site) but he builds the AR-15 platforms for the National matches at Camp Perry Ohio
Here is one of the testomonials from the site with a Rem 7400 that is the upgrade of the 742 that I sold.
I have a few friends who are "snipers" and they think the bolt action is the only way to go for ultimate accuracy. I tend to agree, but I guarantee that I can give them a run for their money with the rifle you provided at ranges up to 500 meters. I told them I got the rifle to shoot deer, elk and hogs so there would be no need for me to shoot beyond 500 meters. When I received the rifle I shot 20 rounds through the rifle and adjusted the scope, Nikon Buck master with bullet drop compensator. By the second box of shells I was shooting groups where all 3 rounds were within a 1/8th of an inch from each other at 100 and 200 meters. Before the upgrade you provided my, I could barely get the rounds to come within a 5-6 inch group at the same ranges.