BFG All Terrain T/As are my chosen off road tire. It isn't the best for mud, it isn't the best for rocks, it isn't the best for sand, but it will do all three reasonably well, perform well on the street without all the loud noise of a tire that actually is great at any of the above mentioned tasks, and compared to the better rock crawling tires I've had, they wear like iron.
You can get AT T/As in almost any size, so finding the right one for the Mite shouldn't be too hard. Don't go too big since too much extra unsprung weight might overstress a driveline that is full of u-joints and the stock size tires already are capable of being stuffed almost to the bottom of the fender in the front.
My modern jeep can "droop" and "stuff" its tires way beyond stock since it is built to allow the axles to articulate as much as possible while in the rocks. The Mite does have a limit, so I wouldn't get crazy thinking that one will be able to do this.