A flyover sounds like a good approach because it must get hot in there without cross flow? Do you need the entire deck covered? You could move the front back a little so it aligns with the shorter side of the house ... or just a bit to reduce the cantilever requirements? Or you could run the front on an angle from the long section of the house to the short section.
Just some thoughts. I know what it's like to agonise over these types of details but it will look great when it's sparkly and new.