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Since you have a .270 and it's based on a 30.06 case, I would personally go 300 Win Mag. If you choose 30.06, might as well take the .270. With the right bullet, it would work. With a 06, you gain the ability to use heavier bullets over a .270 but the .270 is a very capable round. I would take the 300 because you can run a heavy bullet faster than a 30.06. But I know me and a hunt like that, I would second guess myself on bringing enough gun. I agree with staying away from wildcats unless it is something you really have been wanting. Getting a wildcat for one hunt doesn't seem practical.

Edit to add:

Wait, I confused. You said .273... do you mean .243 or .270? I would still do 300 Win Mag but if you have a .243, then the 06 will be a big step up. You would give up too much velocity with a .308.