I would think the Sierra 300 grain MK and Barnes TSX bullets.

Check this site out

http://longrangehunting.com/ubbthreads/ubbthreads.php

Plenty of people on that site with 338/378 and 338/416 Rigby Improved and barrels 36 inches long (91 cms) and 2 inches (5 cms) in diameter. You will also find people there that have the 338 Lapua Improved in bench rest style rifles and they also have the CZ/BRNO in the same calibre as a hunting style rifle.

Also plenty of people doing the same style of thing but in 30 Lapua Improved, 300 Rem Ultra and 30/378 and also 338 Rem Ultra.

I had a 338/378 when it was a wildcat and it was a rebarreled 416 Wby Mark V with about the same barrel contour as the 416.....it was .72" (18 mm) at the muzzle.

Mike