Skinny Shooter,
Go here:
http://club.guns.ru/eng/norma.html
Says a 106gr bullet goes 2800+ which ain't too shabby. Chamber may be a bit much $ wise as the Norma reamer may not be just laying around on the table, but maybe a good smith can do a workaround.
I'd seriously shifting the money from reamer etc to smithing and barrell. get one of your better smiths to install something like a 3 groove lilja in 243, AI if if ya want. Get the correct twist for the bullet weight you want and shoot single shot. Also stretch that barrell out a bit to like 26" that'll help with velocity but probably put some dings on the inside of the vehicle as you're driving along and see the chuck on the mound, hit the brakes and grab the rifle.........
You may want a couple of detachable mags full of shorter rounds just in case the chuck charges from beyond 600 yds when that first shot doesn't go just right.
Good luck, springs a commin, that snow's gotta melt one of these days