Have you thought about a used Winchester 94 Big Bore in .307 or .356 Win? Either one would fill the bill, with the .356 probably coming close to perfect for this application. I'd hesitate to go with the .308Marlin, as the cartridge hasn't caught on yet, and ammo and brass may dry up. Winchester still makes .307 and .356 brass, and you can find rifles in this caliber if you look hard, and they are usually affordable.
The .356, loaded with 180 or 200gr flatpoints would be great for deer, and for shooting moose 220gr and 250gr bullets would work very well.