Savage had the 110 in 338, but from experience, I think you may be hard pressed to find a rifle in those calibers in the 8lb range.
I've heard mixed reviews of the Savage 338. Strange because in general Savage makes very good rifles for the money.
If I had the scratch to build a custom rifle I'd look to someone like GAP, Tac Ops or another high end builder. I don't shoot well enough to take advantage of a custom built precision rifle, though. My factory barreled Remington 700 is more than accurate enough for my purposes.
I would suggest checking out the Snipers Hide forums. There is a lot of knowledge there about what to look for in a custom builder and they'll be able to steer you to a reputable shop. Whatever you do, just make sure you save up the money for a high end scope. If you're going to be dropping the cash for a custom rifle capable of extreme accuracy you really need to spend at least the same amount on your optic as you do the rifle. A high quality optic with a factory rifle is better than a custom rifle with a low end optic.
Edit: I just saw that you would like to also use this for Elk hunting. Personally, I'm thinking a rifle used for long range steel shooting needs to be fairly heavy to absorb recoil if you want to be shooting those larger calibers for anything more than a few shots at a time. A rifle like that might not be too pleasant to hump around the mountains chasing elk.
