Can you clarify if the 10.5 lb is with optics, ACI, level, bipod, sling, and if a carbon barrel is in the budget?
The 338 Excalibur
will be the largest piece of brass you can put a bullet on top of without going to a Cheytac class action. 3082 fps with a 300 SMK and a 31.25" barrel was were accuracy was found for mine using H50BMG. US869 and WC872 yielded more velocity potential, but I haven't invested the time to see where accuracy came together for those powders and that cartridge.
Jamison now makes brass for this round. I got dies from Neil Jones. Simply stated, it holds 140 grains of water vs. 126 in my 40 deg 338 LMAI
. In longer barrels/slower powders, it will outstep the Lapua Improved. In shorter barrels, the velocity advantage slims down some, and if you factor in the cost/brass life of the Lapua brass vs. Jamison, the edge goes to the Lapua in a 28" barrel.
I believe Dave Viers has built some 11 lb Cheytacs using carbon barrels and Lone Wolf Stocks, so you may want to give those folks a ring before ruling out the Cheytac option for your goals.
Since he's already connected at 1350 yards (hats off to that, as that is a ways, and involves many variables that he's obviously has nailed down), he probably also realizes that at those distances, each 100 yards becomes a new monumental task to be successful at cold bore first round hits. I know I simply don't have the skill (yet), to manage recoil of a 10.5 lb rifle for 1350 yards cold bore first round hits.
For now a rough rule of thumb I've come to appreciate when building a rifle towards a specific precision goal is.... 100 yards for each lb of rifle (ready to shoot), so a 1 mile gun for me, would need to come in around 17-18 lbs. My 30-338 Lapua pushing a 210 Berger at 3300 fps comes in at 12 lbs, and I feel confident with it in ideal conditions to 1200 yards. The 338 LMAI is a new to me rifle, but it comes in around 14.5 lbs, and I can see me capping it's potential at 14-1500 yards. There's just a lot going on during that recoil impulse to manage perfectly everytime in my book...especially when you're talking 300 grain bullets at 2800-3000+ fps. Certaily there are folks that can shoot light rifles way out there, I'm just not that good. This is just my two cents, not looking to mash any toes, or offend any light rifle LR shooters/hunters.
I'll post up some more once you post the answers to the questions I posted on the first line of this lengthy post