Sounds to me as if you are on the right track.
Ain't nothing adverse about the 25-06. Especially the AI version.
My personal preference for a barrel would be a Lilja #4 contour. That would be just a schoshie bit sporter barrel and a length of 27". I only say this as I have a 270 WIN with such a barrel on it and she approaches WSM velocities and is good on the animals of which you mention out to 850 or so, NOT including the elk. 5 or 550 on the elk would be a max range, I think, unless he was fenced in
With your better BC it should reach out and do some touching.
Good luck and good hunting.