Thank you all for your ideas--please keep them coming. I'm over 150 miles from the closest fabric store other than a Walmart which is why I asked on here. Anything I purchase will need to be ordered. My concern is I can't use high heat to fuse the stabilizer, and most of the descriptions I've read do not provide the heat setting used. I did use a pressing cloth to press most of the folds out of the deconstructed ties since my iron doesn't even provide steam at the poly/silk temps.
I hadn't thought of using starch. All I can find locally is the spray, but it is heavy starch. Do you think two applications might work?