You're talking about a custom rifle, at standard hunting rifle prices. If I were you, I'd want a Remington 700 BDL Varmint in 7mm-08, .260 Rem or .308 Win with a 6-24X +/- Leupold. However, even that will set you back more than you thought.
Next down might be a Tikka T3 Hunter in .308 Win, with a 4-12X Leupold. Accuracy potential is pretty much there, but lacking target-quality repeatability, due to stock forend shape and heavier weight that makes shooting longer strings at the range more comfortable.
Maybe, get a sporter rifle now, and get a Mcmillan or other long-range target rifle stock for it later?
Maybe just buy a rifle that suits more of your shooting needs now, then buy another rifle to hunt with later?