I was thinking of a fun subject to discuss. Let's say you have a chance to buy a custom hunting rifle that is broken in, has a load developed for it, and has less than 300 shots on it, what cartridge would you want? This rifle will basically be an all around hunting rifle, capable of shots out to 800+ yards. It will not be fancy or built for a specific role. The rifle will weigh less than 10lbs scoped, have a 26" barrel, muzzlebrake, and built with high quality components. If ammo and reloading components weren't an issue, what chambering would you want? Thanks!
Really the choice of caliber that you build this Goldilocks rifle really turns on the weight of the bullet you want to shoot.
At 115-131 a .25 cal 25-06 for me, 257 Wby for others
At 140-156 it will be a 6.5 of some sort. For me a .264 WM. 6.5 PRC for others
For 150-170, a 270 Wby
160-190, a 7mmRM or 28 Nosler
and so on thru the 30 calibers and maybe the 338 world.
The key in all of this is to choose your bullet weight then find the bullets that give you the highest performance for that weight and build your barrel with the prescribed twist and jump for your bullet choice.
Lots of capacity choices for brass but I do not favor overbore cartridges.. and I do favor off the shelf brass. For me that means I can stay with -06 length brass all the way to 338 and wouldn't give thought to 6.5-300 Wby, too much overbore. The 7STW is on the edge of overbore, so the H&H lengths for me start w .300 & .340 Wbys. I have them both and they are spectacular performers. But I also have a 1:8 twist 264WM , 26", and it is also spectacular. (btw, this is a caliber that factories still only offer in a 1:9 twist. Someone is asleep at the wheel. Winchester offers a 6.5 C and a 6.5 PRC w a 1:8, but the 264WM is still 1:9. ***?)
The 7mm Rem Mag may be the sweet spot. Mine shoots 175 Nosler ABLRs. It is a pre-64 Model 70 .264WM w 26" bbl that I rerifled to 7mm with a 1:8.75 twist, 8.5 lbs. Pretty close to your parameters. If I have to choose just one, that's probably it. Enough bullet weight for anything in North America.
So many off the shelf combinations are now available that wildcatting is no longer necessary like it was when I was young. If you are wildcatting, it's not cuz you have to, it's just for your personal fun.
So choose your desired weight, find the best bullets for that category, and build your barrel to suit them. That is where the round lives. The rest of the rifle is a supporting act. Assemble it to your aesthetic.
Buena suerte.