First look at who is shooting what at local matches. Many Fclass matches are too small to split F(O) from F(F) thus your 308 will be competing with 6.5'
s and 6's. Fun but you will quickly see why we shoot these cals.
If you are set on the F(F), then get a Savage 12FV/FP or whatever stock style floats your boat in 223. The ballistics are identical with the 75gr Amax/Berger and you save ALOT of money and recoil. 1/2min accuracy should be attainable with bedding and load work up.
The accutrigger is also very nice and can be tuned to 1 - 1.5lbs. Rems cannot be set that low in factory trim. The more you shoot, the more you will appreciate crisp light trigger pulls. It really matters....
Once you have shot this for a while, you can easily modify it with stocks, triggers, barrels. The Savage is very user friendly to modification.
There is zip for the Mossberg now and unlikely in the future. My guess is that you will have a heavy trigger with likely has no replacement.
For $100 or so more, you can get a Savage and have a great platform to build from.
I also suggest looking at much better optics. You need something that has good resolution, magnification and turrents. I compete with the Elite 4200 6x24 AO scopes and strongly recommend these are a place to start. Nikon also makes decent glass for the money. Burris rings w/inserts and possibly a canted base - EGW or Farrell.
There is so much more but this is my thoughts to start...
Here is one in the EE for $950. A much better choice.
http://www.canadiangunnutz.com/forum/showthread.php?t=256896
Jerry