There is a 300 win mag barrel for sale on the classified forum.

7mm is .284" and is the diameter of the bullet. In OK, when people say 7mm, they are usually referring to a 7mm rem mag.
Other 7mm's include 7-08, 7x57, 280, 284 win. 7wsm.

I probably agree about the 338 wm if alaska bears are included. I'm sure a 300 wm is alright if you have another hunter with you with as a backup.