Have you considered getting some flat metal rods/stakes to attach to the underside of the kammback? They would be flat, almost unnoticeable and would stiffen the thing more than enough.
OR you could bend the corners down a little bit, with V creases in the top surface. This would strengthen it a lot as well as help it fit template.
I'd be very interested in a tuft test of this to see if the airflow is attached, and what the fins are doing.