No need or benefit to the carbon barrel. Buy a well crafted barrel in the right contour. Save your weight in the quality action and stock. It still requires solid bedding and assembly to function properly.
Don't forget about ring, rail and scope choice. This can also make a big impact on weight. Don't sacrifice a few ounces for #### rings or bases that don't line up properly.
If your hell bent on weight, TI action (PGW is not a bad option), by the time you pay to have a rem action turned into swiss cheese, which also reduces the actions strength.
Good luck on your build. You have some great possibilities. If you are on a budget, look into the savage action, quality barrel and stock. If $ doesn't factor into it, the world is your playground. Fly at er!!
I ended up going with a straight up 284 Win over the 6.5/684. With some of the new powders out there, its hard to outclass the 7mm high BC bullets.