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.

Unfortunately we can't see the spline in those pics.

The first image shows it pretty well from the top. The second image show the spline peeking out from the side. Unfortuneately the top and bottom pictures are from opposite sides, but it gives you the general idea. I decided to reuse the original holes to avoid weakening the attachment points too much. The shelf recess does not show very well from the top view, but it is there and the joint is pulled pretty tight.