OK, don't panic. First off, no AR15 parts for free float tubes will fit. ZERO. Free floats mount using the barrel nut and the nut on 308ar's are way bigger. You mentioned carbon fiber…. you mentioned longest sight radius…. here is my plan for you, no holds barred, for a competition 3gun rifle. http://store.lancer-systems.com/lch7-extra-long-15-cooling-slots-no-rails/
Here is your carbon fiber handguard, that will cover the lo profile adjustable gas block you should buy to replace the one that you had. This will :
Allow you to put a rail at the end of the guard to mount a rail mounted ft sight, giving you the longest sight radius possible.
Also give you gas adjustability to fine tune you rifle for the rounds you are using for 3gun.
Buy a heavy buffer from Heavybuffers.com, which will reduce recoil and improve your ability to keep your eyes on the targets in transition.
Get a Geiselle 3gun trigger. Fastest reset out there. It's a two stage that feels like a single. It's slick as bat shit!
Ask and ye shall receive. If this is truly going to be a 3 gun rifle, you will need to update some parts to really get her going, and per your specs this how I'd go. Also consider doing the work yourself, if you have any mechanical ability, doing the work is easy and will allow you to be more familiar with your rifle, and allow to change out parts to tailor it to your desire without paying a shop, or letting them butcher it and say "uh-oh". DUMBASSES.