I second the sabot idea. I think I'd pick the highest BC solid I could find, since you will have plenty of length in the sabot to play with and they ought to hold up in flight, and use a 300wsm or similar cartridge. Since this is your money I'm playing with, a gain twist Bartlein or similar with as much length as they can provide would be the barrel.
EABCO still sells the sabots and seater dies.
Sabots have their place but long range hunting is not one of them. The problem with them is stability due to rotational deficiency and the fact that when the Sabot releases from the bullet it can alter the bullet path.
Years ago Remington tried this concept in several calibers and they were smoking hot, but at 100 yards they had already lost any close range accuracy. They are very effective in smooth bore barrels and as long as the projectile has fins that will rotate the projectile.
It does solve the problem of rotational stress, but they are just not accurate enough for the type of shooting/hunting we do. It trades one problem for another.
J E CUSTOM
300 RUM 17 Twist 110 Vmax well over 4500 fps, a 308 beside it for reference.
That thing is an absolute beauty!!!338 EDGE 32" 12 twist Barrel 160gr Barnes TTSX 106gr of RL17 = 4200 fps
It's a Remage
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My whole gun and barrel collection revolves around High velocity shooting and has for a long time, I have friends and colleagues that have said that they get bored with a certain rife or caliber that they have. Let me tell you this that thought has never crossed my mind with any of my rigs.
Dean