Hmmm... I don't think I ever saw an answer to what distance you intend to shoot primarily. It does make a difference, in my opinion.
If'n it were me... I'd say if the *majority* of your shooting is going to be @ 600yds and in (i.e. you might only get to a true LR - 800-1000yd - match once or twice a year), get a 6 BR, Dasher, BRX or something similar. The wind advantage of the big heavy bullets isn't going to outweigh the lower recoil, lower cost, longer barrel life, and sheer accuracy of the small-to-mid sixes.
If you are located where you could conceivably expect a reasonable split between your mid-range and long-range shooting... I'd say one of the mid-sixes (6 Dasher, 6x47, 6CM, etc.) or one of the mid to large 6.5mm (6.5x47, 6.5-08, 6.5x55, 6.5-284) calibers. As Kevin Thomas pointed out, the 6.5-284 has an excellent reputation for LR accuracy; the US F-Open team didn't pick it by accident. It is a bit of a waste, in my opinion, at the mid-range distances. More than a few shooters won't pull a 6.5-284 out of the case until the range goes *over* 600yds, as barrel life tends to be short enough and the ballistic advantage small enough that it just isn't worth it. Its not that a 6.5-284 isn't accurate enough to win at the closer distances, but it's not really being used to its full effect.
Finally, if you live near an active 1000yd range... it might be very much worth going with a bigger caliber. They do get more difficult to shoot as accurately, and depending on how you go about it, they can get dang expensive to shoot as well. Some of the combinations that are in use such as 7WSMs and 7RSAUMs that are loaded *very* hot (B180VLD over 3100fps) have barrel life (500-700rds) that makes a 6.5-284 look good. One of the guys I watched @ the 2009 FCNC was punting B210VLDs out of a .300WSM... dunno what the velocity was, but he was actually using a vertical grip on the fore end to control the jump & torque. Not my taste, but its an option. Of these bigger calibers, the .284 Win and .284 Shehane (improved) seem to be gaining interest - Charles Ballard has won two years in a row with his as well as setting the standing record @ 1k. The same B180VLD @ 2800-2900fps with markedly better barrel life and less recoil, plus Lapua brass (6.5-284 necked up, oh the irony
) to boot. Charles also lives fairly close to the NSSC 1000yd range @ Camp Butner in NC - so he can spend as much time as he wants at the 1k line. Somehow I doubt he'd field the same rig if the majority of his matches were 600yd and in.
Someone mentioned going .308 instead... and I do think that might be a viable option. If the rifle is a Savage (thought I saw it mentioned as a 110 somewhere in the tread), then barrel changing is extremely easy, and you probably already have a .473 bolt face... so changing the barrel to a 30" .308 medium or fluted heavy Palma contour with a twist between 1-10 (for 210gr bullets on down) to 1-12 (probably 185gr bullets on down) would be no problem at all. The barrels last a bit longer than most of the options mentioned above, less crap to carry around (no front rest, etc.) and pretty simple to get up and running. The F/TR class is less about equipment and more about who reads the wind better - and anyone can learn.
YMMV,
Monte