I ended up going with the three versions shown below. The other options I tried weren't worth the pain. As it turns out, this stuff can be quite finicky. When the prop loads, the buttons need to be close to and parallel to the piece of fabric they're supposed to attach to, and the top and bottom placket can't be near overlapping where there's no button, or bad things will happen in the cloth room.

Now these here I tested quite extensively, and they look very well-behaved to me. So, I think I'll just finish up the materials now, and then it's time to package everything up so it can be released. Thanks for everyone's patience!

-- I'm not mad at you, just Westphalian.