The Ascot actually does well offroad up to it's limitations of a low exhaust and oil pan. I have done some exploring in the area and after today starting to miss my XR650L again.
I'm running the Shinko 705 on it now and had a Kenda K761 last time. I had a thought of a Dunlop 606 but as little as it goes in the dirt I stuck with an 80/20 dual sport tire. They are good in the rain though.
these are from a little offroad exploring a few months ago.