I had some leftover vinyl from other craft projects (like this) which should do the trick. Then I checked out my local craft store's home dec department. Lo and behold they carry the same pins that vendor uses for just a couple bucks.
The benefit of these pins is they're easily removable, by twisting into place, and barely leave a mark in the fabric.
So let's see if Lil' Girl can figure a way around this one...