Instead of a .338 Lapua, have you ever thought about a .300 Ultra Mag???
I recently had my Remington Sendero changed from .300WM to .300 Ultra.
with the .300WM i was happily hitting targets out to 1700 yards with Lapua 185gr projectiles, i tried using heavier projectiles but the recoil was too much, after all i am a skinny 6 ft guy, i solved the recoil problem with heavier slugs by putting on a muzzle break, but i believe the better projectiles for the .300Wm are the Lapua 185 gr projectiles as they give great B.C at a good price.
I old army sniper mate of mine had changed his 300WM to .300 Ultra topped off with a nightforce scope and after using that rig, i was truly impressed especially when we were extending our shooting out past 2200 yards.
We had looked at using .338 Lapua, there bigger rounds and we found that with using the .300 Ultra we were saving money in reloading and still doing the shooting that we wanted to.
So alot of us who are serving in the NZ army as snipers and those who have retired but still stay in touch with the unit all have rigs other than what we were using while in the Army. We are always on the search for a better round and i personnally believe i at least have found it with the 300 ultra.
No one to my knowledge has a.338 Lapua, not yet anyway but there are quite a few .300WM's, 7mm STW, .300 ultra Mag and some other wild cats being used.
But remember other than the calibre, you also need good optics, i have just ordered a Nightforce scope as they give clear resolution and give me the minutes of angle for right out past 2200 yards for which i could not get with my weaver, with my weaver 6-16x i had to have hold over past 1700 yards even though i was already using shims on the scope rings.
What ever your choice, happy shooting.
Farmer