Re: add stock weight
First off don't turn your nose up at the 308 as it is a greta preformer at the 1000yd mark with the right bullets.
Second , I would bed one or two Harrts Rem 870 Mercury Recoil reducers into the but stock of you gun , they help alot with soaking up recoil and they weigh in at about 1lb each , their 4" long and 1" in diameter so at least one would fit. , then if more weight is needed you can mix some lead shot with 15min Epoxy and fill in the butt as needed.
Take your favorite 308 and load some 175gr Berger VLD's and give those a try at your longest range , you'll be suprised at how flat they shoot and hold their velocity.