Re long range rifle competition, not this "F class", I used to shoot 1000 yard competition at Camp Perry, Ohio, excluding the Nationals, the Ohio
Rifle and Pistol Association used to have regularly scheduled matches at Camp Perry. these included both The National Match Course (200, 300 and 600 yards), and 1000 yard matches fired with "service rifles", back then they were Garands and M1A's , some still fired Springfields. NRA Match Rifles were bolt actions, fired with "iron sights" or scopes, as per the match program.
Also fired NMC and Long Range competition at Quantico MCB, and Stone Bay, Camp Lejeune, Jacksonville, N.C. There were regularly scheduled matches at these locations, also Cherry Point MCAS, Havelock, N.C.
Re Quantico, check with MCDEC there, or contact the base itself. Ditto for other military installations, which usually have a "Rod and Gun Club" on post. I'm no longer active in high power rifle competition, however I would assume that shooting goes on at these locations.