How about a Savage Lightweight Hunter in 308 with a 24" tube, the only drawback is it's a wood stock....but it's oh so light. Magazine fed, spiral turned bolt accutrigger accustock and mine with a 30mm Vortex Viper PST 4-16 comes in at 8.3 with 3 in the belly and one in the receiver.
Of course I rebarreled it and restocked it (Bartlien and Manners) and it's now down to just under 8 with the Viper thats getting taken off and replaced with a Diamondback SF for another 10 ounce drop. Its so light, a strong wind makes it flutter....
You don't know it's on your shoulder....lol
It shoots too. It shot good stock, it shoots lights out now. sub moa at 200 consistently.
I like my 308's and I like Savages, I have a bunch.... No regrets.