You'd be hard pressed to find a bigger 308 fan than me, but elk at 600 is really pushing it.
Yep, I tend to agree...I have great fondness for the 308, and am in the process of building an 8th...super light, short barrel.
But I have another specifically for LR with a 30" heavy Palma 8 twist, long action, aluminum chasis using hybrid cases it can run 168 gr 3250 fps, 200 gr over 2900fps, 225 eldm to over 2700 fps.
Lapua cases about 50 to 100 fps less than hybrid cases, with heavy bullets. A 200 gr .715 BC SMK at 2856 Ave in Lapua brass would get the energy and velocity, in a heavy to carry long action, very accurate but 14 lbs....and match bullets are supposedly not recommend but many use them. But you can seriously bump up the performance of the 308 case, if you insist on high performance from it you're gonna have to carry a heavier rifle, long action, and a slim profile 28" with 9 or 8 twist barrel, will be light enough to do the job...I run a 27" 308 for a varmit rifle with a Remington Sendero contour for varmints, easy to carry...or a 6 Dasher not so easy to carry.
But 600 yds on elk, is really pushing the average configured hunting 308 ...I'd just stock a little closer and not worry about it...no reason to take a 600 yd shot, if you can easily walk another 300 yds, and make a fairly easy shot. Many yrs bow hunting makes a lot of LR hunting seem, silly.
When 50 yds is a long shot, most are between 8 and 30 yds.
But I enjoyed LR shooting for 30 yrs, at varmints and targets...but hunters should try to meet the velocity and energy requirements for a fast kill on big game as bullet performance falls off fast as velocity drops off, below 2000 fps. Example you can wrap a egg tightly in plastic wrap and shoot at 1000 yds with 3000 fps muzzle velocity from a 308 it will take 2 or 3 hits and not explode...but just puncture 30 cal holes in the egg, the thin plastic wrap holds it together, and 150 gr Nosler BT still have the green plastic tip intact at 950 yds, just a pristine rifled bullet.