I was facing the same issue as you. I had Kriby build me a 338 Lapua that I just received, I have yet to test it, but he really did a great job! I went with a BAT action with the Badger DM. His raptor action would also be a great choice, but I was looking at a 10 1/4 lbs rifle for hunting, but that could still reach out there, well, he built it and if it shoots as well as it looks, I'm golden! The barrel is 28" and has his PK muzzle break. I choose this break after watching a demo on YouTube. The rifle it's toped with a NF NSX 5.5-22. I have some rounds loaded up and hope to get out this weekend to shoot it.
Hope this helps.