How should I build up stair stringers (instead of cutting them out)?
Our wood working site might have some good ideas.
If I was doing this, I'd be gluing the triangles to the 2x6  and then use dowel rods, one vertical and one horizontal, for additional support. You could also use screws depending on how you wanted to finish the stairs. Since you're reclaiming the triangles, the dowel rods might be more appropriate.