My 2 cents...
The only advantage to a Knoxx stock is to absorb recoil so if you are going to put your action into a one... get something that really kicks, not a 308 or a 223 - something more like an unbraked 300 weatherby mag, 300 win mag, 7mm stw, 300 RUM (7mm RUM if you plan to reload.) 338 RUM, etc.. I'm not sure how that stock will do long range though.
If, however, you really have your heart set on a 308 or 223 because you want zero recoil go with a Macmillan or a custom laminate stock with a brake. These won't cost any more than the knoxx but will be much better for long range hunting (in the 308 not the 223, but that really depends on what you are hunting.)
As far as a "custom for $1000" gun goes, I don't know of anywhere you can get one for that price - unless it's been shot out.
Another option to consider accuracy and price wise is the Tikka. I've had great luck with these guns. Here's a link their list of calibers currently imported to the US: TikkaUSA
Savages also have a good reputation for out of the box accuracy, which is crucial for long range hunting, and are within your price range.