Just did the same thing in 338 RUM and ended up right at 10# w/scope and sling.
I Hmmmmm, because I would be hard put to reduce the contour and length of that barrel and twist because I think that the barrel would be worthy of a truly long range rifle. Something like the 338 Edge and shoot the 300 SMK as you desired or the even heavier Wildcat pills.
It is my opinion that a 338 RUM barrel needs to be no longer than 26" to wring max velocities out of it. I've also found that 30" + brake is too long for a carry gun. 27" is even too long IMO. 24 to 26 length seems to be about right. In addition a heavy contour 30" barrel is hard to hold steady for long for an off hand shot and useless for a jump shot. With the Edge and 300 SMKs you could shoot from the north end of Washington county into the south end of Butler Co. easily. With the 338 RUM your range would be limited to the North Hills area. (a little humor there)
My 270 AM has a 30" #7 Lilja fluted with Defensive Edge brake, carbalite stock, Leupold bases, Burris signature rings and Supersniper scope and weighs in right at 12#. But it sure isn't a carry gun. In fact I drag it pretty much where ever I go and set it up an there it says.
Here's some pics. It looked really good with the flat black stock, and just unique after the long hair'd guy with the chain saw blade neckless at the paint booth a the local fair put the Krylon to it. But hey, it was fun and she still shoots great.