My aunt is a taylor, I gave her homework to find me some fabric with the necessary qualitiesShe gave me 5 or 6 samples, one of them was perfect. But the material is used for protective bags (not sure what is the right way to call them) for sunglasses. It's a bit elastic and makes nice folds. I used it a few years ago for Senate duel Palpatine... So mabe you could change in some optic stores?!
I found some 10" x 10" black microfiber online. Comes in a 10 pack so I'll have some room for trial and error. Just need to get a circle to help with the cutting.