We recently built an open riser staircase out of white pine. The stringers were 4"x14" and the treads were 3"x12". Through mortise was 2"x10" and wedged with similar red oak shims in from the edges about 3" . The tenon was centered. Wasn't actually a dovetail joint, as we glued it also. Our concern was splitting of the treads so we weren't to aggressive pounding the wedges into the 1/8" kerf. We didn't house the joint because of shrinkage concerns. Biggest difficulty was the mortises. We bolted the stringers together with exposed sides out and then drilled from outsides to the center.
That's how we did it. Good luck on your project.
Mark Surnoskie