You've got Kraig and Steve and "guntotin" with first hand experience here and I'm more inclined to listen than to offer an opinion. I have never shot a moose. I will offer something from Craig Boddington on the subject for your reading pleasure.
For what it's worth, Col. Boddington says that .308 and .30-'06 with heavy bullets are the "absolute minimum that make sense for Moose", saying that the .270 can handle them but that he's not inclined to err on the light side. Can't remember what O'Connor used to say. Scandinavian moose are said to be a smaller breed. Most of the time when I see Craig shooting something on TV, it seems to be .338, .375, or something that starts with a "4" that I wouldn't enjoy shooting.
With no relevant experience, I'm just reporting.
I seem to recall that a lot of Canadians used the .303 British successfully, but that's a lot closer in power to the '06 than to the .32 Winchester Special, which was reportedly designed to work better with black powder than the .30-30 in the Model 1894.
When I was a kid and neighbors used to hunt deer with Marlins and Winchesters, many used the .30-30, but one really thought the .35 was a better tool for the job. Maybe that's the source of my nostalgia for the Model 336. Later, bigger cartridges started to gain favor. Going against the grain, I'm a .257 Roberts man. Recoil. Today my rifle shooting is confined to paper targets.
I'd be interested in how this plays out.
You can now get LEVERevolution loads for the .32.