Well I pulled out the panel this morning and began tracing the pieces on to wax paper. I hadn't realized just how many pieces there were in the panel. And that parasol is going to be work. What I want to do is cut one piece for the "fabric" of the parasol and then overlay the "Ribs" of the parasol over that so that it looks cohesive.
I think I'll be making black cord "ribs" and couching them to give it a really nice look. I hate having to try and pull through the seams to make cord but I think in this case it's the best answer. What do you think?