Just for pure convenience, low cost and it works. I took some heavier craft foam, about 5 mm, and made a fly patch which I attached to the back of my hat with some heavy thread at the corners, I may have added some light leather underneath for durability. It works well and I have never forgotten to take my hat unlike most other things I use fishing. I have a similar one on my "winter" hat.
Hat fly patch 1.jpg