Thanks for the help everyone. I have a solution that I just finished installing yesterday. I went with the "free tenon" or "spline" approach. I had all used timbers, but I am pretty happy with the results as that it looks like the patch belongs with the building. Everything fit pretty well and ended up amazingly square. I have included a pictures below. I would say not too bad for my first timber framing project. All I need to do now is install braces to the main wall. I found a good article on how to install braces after installation.