Legolas, my question would be are you going to be hunting this place that allows shotguns only once or twice, and then go back to a rifle area, or a lot?
If you'll just be doing this once or twice, I'd try your single shot 12 gauge with Federal Tru-Ball slugs, they shoot very well in most smoothbore shotguns. If your gunsmith can put a little white bead halfway down your barrel, you'll find when you line up the centre bead and the bead near the muzzle, your accuracy on longer shots will be much better!
If you're going to be hunting deer a lot with a shotgun, I'd get a pump action 12 gauge that you can get a rifled barrel for with a cantilever scope mount. With a scoped, rifled barrel rig shooting sabots, you're good out past 150 yards. The other smoothbore barrel you can use for birds, and it would still be a good idea to have a white centre bead mounted on it...makes long shots a breeze.