Smitty,
Unfortunately, to the best of my knowledge, Weatherby is the only current company that manufactures rifles in the .338-06. Your only other option is to either look around for used rifles, or, have one custom built.
I agree with your assessment of the 338-06. I personally own a .338 Win. Mag with a muzzle brake, which thus has increadible power and kicks less than a .270, but a 338-06, even without a muzzle brake, would make a great rifle for just about anything in North America. It is not really a flat shooting rifle - so forget about antelope hunting out west with shots at 400 yards, but it's great for just about everything within about 200 yards.
Zachary