Are you taking horses??
By all means take both rifles that you mentioned.
I have hunted and guided for elk most of my life and have been in on over 100 elk kills. Very few have been inside of 200yrds during rifle season. (a couple at 7yrds during archery)
The mature bulls are WAY bigger than the cows but they are not bullet proof. (well some seem to be a little resistant.
) I killed a cow at 6o yrds with a 22 LR pistol..Two shots to the ribs and she troted off for about 40 yrds and fell over.
Your 250 TC will work great! I've seen the comercial where they are smakin' the 6" plate at 250yrds with that thing... It is nothing that should be allowed in any "Primative" season anywhere...but it is dam sure a Fine weapon.
In you '06 you should shoot either the 165 (to extend your range a little) or the 180.. Either one you choose, make sure you go shoot it at really long ranges just so you "have" an idea of what you and your gun can do.
When your giude asked "Can you hit him that far??" you will be able to say "Sure, I have been shooting the 450yrd plate for six months" or "No way, I have been shooting at the 450plate for six months and still can't hit it".LOL
A
wounded animal should be shot at at "ANY" distance if he can still be seen and for as long as it can be seen.. yes I have seen the "Hail Merry's" bring down wounded elk at way over 1000yrds...just walk em in there.
Take pletty of ammo!! Guys always seem to run out if things get exciting.. A wounded bull will often "LEAVE" the country..(and I am not talking a mile or two) I mean Leave... Shoot them until they are down!