B23
Gold $$ Contributor
X2!Id be looking at a 338 for that distance, seriously.
With regard to recoil, a rifle "Purpose of the build is long range shooting out to 2k yards" as the OP describes, if it were me, would be built heavy so even in something 338, recoil really wouldn't be an issue.
My 338 Lap Imp if I recall weighs a little over 18lbs and even shooting 300gr bullets it's a pussy cat to shoot. I used to have a Weatherby Accumark 338-378 that was considerably lighter. It definitely had more felt recoil then my 338 Lap Imp but it wasn't terrible. Build a 338 with some weight to it, put a good brake on it and you'll be pleasantly surprised how much it tames them down.