What caliber(s) will take down everything I could hunt in North America out to say 400yds?
By including (perhaps inadvertant) the Great Bears in your question, you will likely get cartridge recommendations that either:
** overlook your including these heavy duty animals (at the range you indicate), or
** are going to suggest "more cartridge" than what you really need for what you are likely to hunt.
I'm guessing thatsomething in the range of a 7mmRemMag, 30-06, or300WinMag would do nicely for you. If you get around to the $15-25K Great Bear hunt then obtaining a different riflle for the job should be of little significance.
If you meant it just the way you said it, then 340 Weatherby Mag, 338RUM, 338 Lapua, 338-378 Weatherby, 378 Weatherby, 416 Rigby, or 416 Weatherby Mag. This latter group is a
significant step up from the ole thuty-thuty and certainly are not gallery guns, so consider trying them out with someoneknowledgable and that you can trustbefore you pursue one of those.
In any case, your guide will not likely let you shoot at a Brown or Polar Bear at 400 yards (or even 300 yards).