I was searching and found a couple of threads by the same guy who has built a sub 4lb!!!! 308 AR. It has a lot of exotic parts but I think 5-6 lbs should be no problem. Especially if I sbr it. Maybe shoot for 6lbs all up with an Aimpoint micro and a full mag.
Probably Breastroker I'd guess? He's built some neat stuff, and I had the pleasure of helping him with machining on a couple parts; great guy.
I would lean toward building something like that as well, but for the guys who want to just buy something, look at the Balios Lite 308. You'll pay for it, but they did a nice job of building a lightweight 308 AR.
One thing I'd caution about though, especially since bulk is one of your complaints about the SCAR (and I agree) - even a very light weight 308 AR is still going to be bulky, at least around the mag well. There are some options out there using smaller AR15-ish sized uppers and handguards which I like the idea of, but the mag well is still bulky to handle those 308 mags.
I'm not one of those guys who claims 6.5 Grendel is almost as good as 308 (it's not), but if you want 308 range without needing as much power or recoil, a lightweight build around a 6.5 or 6mm/243 Grendel-based round is a good option partly because it can be a LOT less bulky. The 6mm versions in particular can be really flat shooting. You can build something fairly slim and stay around 6lb even with a 20" barrel without going too exotic on parts, and lighter than that if you want to go nuts like Breastroker.