I'd recommend either the widest knobby Rene Herse tire (though short of snow or uber mud, it really is amazing what can be ridden on their slick tires), or to go wider yes, Schwalbe's Thunder Burts or Racing Ralphs are fantastic all round tires (surprisingly good on asphalt too). 2.1 to 2.25" will give you plenty of tire. My Hunqapillar maxes out at 2.1" (it's the first run, so narrower), and that is plenty wide for most things. For reference, I ride roads (pavement and dirt) and trails all around Pikes Peak as well as to and on the Continental Divide.
With abandon,
Patrick