Based on your criteria, you are going to have a difficult time finding a factory rifle that will meet all of your needs/wants. The Sako Finnlite in 300wm is a good shooting light rifle. But has a light contour barrel that will heat up pretty fast. And the recoil is pretty heavy. Probably weighs 6.5lbs without scope. With the scope that you want it would probably put it right around 8.5lbs.
+1! If I can keep my rifle set-up hunt ready at 10 lbs, I consider it light enough and myself lucky.
I too do a lot of hiking when hunting and my average hunting rifles are around 10-12 lbs hunt ready.
With a $2K budget, I'd seriously look at custom rifles or consider re-barreling the Remington Mountain Rifle in 270 with carbon barrels in 1:8" twist ... but that's just me.
Cheers!