IMO you should go with the 7 RUM instead. I doubt you will see much gain with your wildcat but you will see plenty of costs. Custom reamer, custom dies, altering an existing rifle to accomodate the 338 lapua case.
Here is a site I found discussing the 338 RUM vs the 338 Lapua:
http://www.snipercountry.com/InReviews/338UltraPoorMansLapua.asp. The key sentence in that discussion is: The Lapua requires lots of modification to work in a Remington 700 action and that means high cost. The Ultra is a factory available chambering and requires no modification to the Remington Ultra action. In short it can be built for around the same cost as a .308 sniper rifle.
Now if you just have to do something different go for it.