You also have optical quality being an issue, though focal spot size isn't as big a deal for a cooker.
The best idea I have seen is a guy who made a cylindrical parabolic mirror buy letting silvered Mylar hang under its own weight from two rails. I think that was on Hackady if you want to try to find it. That would be dead simple to make work.
Dr. Scott Kovaleski
Associate Professor
Electrical and Computer Engineering
University of Missouri
349 Engineering Building West
Columbia, MO 65211
Ph: 573-882-8377
Fx: 573-882-0397