Are you able to explain the process that you've taken thus far in creating the disc? My brain is in lunch mode at the moment, so it's ability to think outside of the square is currently not there. (I always start with the supports and binding).
I attach you a photo of what I want to do because my millinery vocabulary isn't good enough to explain it, although I'll try.
My problem is how to fix or sew the two wide sides of the veil. My idea after join the two wide sides is fold the veil along and gather it to put inside the wire and obtein the round form. And then sew it to the base.
Sorry about my explanation, I hope you understand me.
Thank you very much