In my opinion, AR-10s are probably the single best candidate for a carbon fiber barrel! Could chop off a good bit of weight there.
I don't hunt with one, just because I've never been committed enough to the AR-10 platform. I run the AR-15s all day long, but for 308+, I am solidly in the bolt gun camp. But if you wanted to go lightweight, you could do it. AR-10s are just going to be an expensive way to do it. But, I'm not judging I've spent money on worse endeavors.
There are lots of good lightweight components out there, it may just be easier to do that build from scratch. 2A-Armament has a 6.75 pound AR-10 platform on the market that looks very interesting (*disclaimer, I have never shot one, and cant speak to them as a solid choice, just that its an option). I'd probably prefer it with a carbon barrel vs the pencil barrel it's wearing... but that's just me. At that weight, it's not much heavier than a lot of the bolt gun options. They sell the complete package for $2.6k+, but you can buy their lightweight receivers for $700 for a matching set. If you piece together your components well you could probably do it cheaper and less weight. With optics, there is no reason you cant have a solid 8-9lb AR-10 platform, its just gonna be way more expensive than a 8-9lb bolt gun for obvious reasons. Shoot, im now thinking this would be a fun project to build...