Rifle matches at Camp Butner are often run by the North State Shooting Club, whose website is
http://www.northstateshootingclub.com/newindex.htm . This page also has contacts, which may be helpful in determining a number of things about matches there.
NSSC's website says the match on the weekend in question ("Jim Fletcher" match) is an over-the-course format event, which for you is problematic. This is because each day's events involve at least four strings of rapid fire (difficult but not impossible for an F-class rifle.) A better course of fire for F-Class is the December 2-4 "NSSC LR Iron Man Challenge" which is essentially 3 strings of fire @1000 yards, with one of Saturday's strings being in a Team match. DO NOT BE AFRAID OF SHOOTING ON A TEAM!!! It is an excellent way to learn about range conditions, under the guidance of more experienced shooters.
One peculiarity about this range: Unlike most facilities, target carriages at Camp Butner are motorized. (At all other ranges in the US I've been on, carriages go down and back up using people power.) While the arrangement at Butner saves wear and tear on most of your body (except for maybe your thumb), they are SLOW - about 13 seconds from fully up to fully down.
Expect to meet world class shooters there - There are at least 5-7 living in the area, plus more who travel in from all over the East Coast. If someone is barbecuing on the range in a BIG cooker, do not miss it! (The BBQ chef may also be a shooter.)
NOTE: The first and only time I shot at Butner was not a match. It was a tryout for the 1999 US Palma Team. (US long range rifle team. No, I didn't make the team.)