I built a Lapua a few years back with your same goals in mind. My rifle is 10 1/4 lbs without the scope. My barrel is a #5 lijia. Although my rifle is extemely accurate, my next barrel with be a #7 or heavy palma. In my humble opinion, 10 1/4lbs is too light for that rifle. You are unable to spot your shots with the recoil, 11-11.5lbs I feel would have been much better. Below is a photo of my rifle. Hope this helps.
I went with a 28" and it's fine. My personal opinion is that a 27"-28" will be perfect in a # 7 barrel. Let me know how the build turns out. I really like this caliber. So far, I have taken an elk at 234 yards and a oryx at 700+ with it.