I don't know about hunting deer but my hunting partner LOVES the 338 federal, he has 3. His family has killed multiple Alaskan animals with them, caribou, Buffalo and dall sheep, but none were at your intended range. When he had to take a long shot (621) on a moose he didn't grab the Fed, he picked up his 300WM.
YMMV but there comes a point where it's just not worth stretching the ballistics beyond what a round was designed for and it's time to step up in cartridge size. My friend is now doing a 338 Sherman Max to overcome the limitations of the Fed.
I find this gentleman's work very enlightening, you might consider his excellent write up on the 338 Fed., which I agree is an under rated cartridge overall, but not really suited to "long range".
.338 Federal history, power and performance
www.ballisticstudies.com