Because the different "strands" of the drapery needed to be different lengths and pinned at different angles, I decided to scrap trying to use the original circular array of rectangles and am modeling each strand one by one... I don't even have the original component anymore!
I think my original issue was the way I was selecting the geometry. I was able to model one of the strands, attaching file.
The other issue I've come across is once I model the cloth, I realize I needed to add more pins, but because I want the pins to be in a circular shape, if I toggle the drape off, I can't tell where to put the pins so they catch the cloth.
Is it possible to add pins after modeling the cloth?
If anyone has a better work process on how to model the referenced drape, please let me know.