I eventually came across a used satellite dish, and with a little bit of modifying this turned out to the be best option for a Captain America shield.
If you are interested in making one of these, you may have to do a bit of searching and asking to find a used satellite dish. I've seen them show up at thrift stores from time to time. Keep your eyes open, and you should be able to find one.
I have a separate instructable on how to make a flyable version out of cardboard and duct tape, which you can check out here: Flying Captain America Shield.
Thanks for looking!