IF I had to have a big game caliber and it was limited to the three major rounds you mentioned, I'd have to go with the .308. Think on it for just a minute...
The '06 and .270, fine rounds that they are really need at least a 22 inch barrel, and either will really shine with 24 or 26 inch tubes. The .308 works well with little noticeable velocity loss in barrels as short as 20 inches. Well, you'll see less velocity loss, maybe that makes more sense. The two bigger cases, to get the highest velocities, need powders at the slower end of the spectrum, meaning longer tubes. The .308, with a shorter, somewhat fatter case, uses medium rate powders with bullets up to 180 grains very efficiently, and needs less barrel length to get that faster powder used up.
As to ammunition availability.....I have done it myself. Several times. Left it sitting on the counter while loading the truck, looked right at it, and walked past it. For the last twenty years, however, I ALWAYS have a backup rifle, even if it's a road hunt with just me and the Super Pooch, AND, I routinely keep a box of .223, .308, 270, '06 and .357 mag in the console of my rigs, as well as stashed in the camp trailer.
BTW, I wouldn't hesitate for a moment to take a Shirras moose with a quality 150 gr. .270 bullet. Elk die very efficiently with good 130's, as well. When comparing the rounds, take a look at the sectional densities of the available bullets. It's an eye opener, if you've never done it. That 130 gr. 270 bullet has a sectional density that compares really closely to the 165 gr, .30's.
I understand the difference in the geographical areas, and hunt tactics, so please understand that "out here" things work a little differently. We hunt whitetails in the same areas that are inhabited by elk, moose, antelope and mule deer. 300+ yard opportunities abound.
