Why not try the Hornady 105 AMAX? It's cheaper than the Lapua, easier to find, and if you work up to the OCW of 48.5 grains of Hodgdon Retumbo--with a magnum primer, by the way--you'll probably get good results.
The 1:9 should be fine with the 105 AMAX. Hornady claims they designed that bullet to fly well from common factory twists. Should make about 2900 to 2950 fps, and has a BC of .500.
That bullet has been very accurate for me to 1000 yards, and a bit beyond...
I'm shooting an 8 twist, but as mentioned, I think you'll be okay with the 9...
Dan