Since you already tried the 338-06 and didn't care for it, I don't think that the Whelen will make you any happier, unless you're going for nostalgia. With the Federal High Energy loads, you can basically turn your 30-06 into a .300 H&H Mag, performance wise, maybe even a little better depending on your gun. You could buy the ammo, pull the bullets, and load another one in it. Writer Sam Fadala does that quite a bit for his 30-06.
You seem to be concerned about the pricey bullets you'll have to use in CA. Then why bother getting a gun that's going to use a bigger, more costly bullet than what you already have to use? Honestly, how often are you going to go moose hunting? Elk, maybe I can see on a regular basis, but moose? No moose in CA is there? Or even that close to you? I guess it depends on what your out of state options are. Anyway, there isn't a moose or elk walking that can't be cleanly taken with a 30-06 and a good X-bullet load. Load up a 200 or 220 grain X, you'll be close in power to the three you are asking about that it won't matter which one you use inside 300 yds. I'll admit, the .338 Win Mag does have more juice, but is it worth having a gun that is expensive to shoot, that you won't shoot regularly, to out do your 30-06? I don't think it is.