The Analysis of Irregular Shaped Structures Diaphragms and Shear Walls by Terry Malone is a great reference for light-frame construction. Your post is pretty vague on building construction type, prevailing code requirements. What is your thoughts on the analysis?

As a starting point, consider your diaphragm to be a beam (either simply supported or continuous over multiple supports with the supports being shear walls, moment frames, diagonal braces, etc.). Construct shear and moment diagrams to see what the forces and moments are at the intersection of the "L" pieces. Decouple the moments into forces. Design the straps. FYI....you may not be able to consider the "beam" as a continuous beam if your diaphragm is flexible.

This was always a concern in the back of my mind when designing large irregular wood diaphragms for seismic loads. Our typical practice was to model it as a rigid diaphragm. However there was typically no consideration given as to how the forces would get from one side of the L to the other.