went to answer but I think you have all the answers that you need and I use the iron on tear away with tear away as well if it is a dense design or just for extra stability then tear it all away together. I have found that if you hoop it all together it gives you a better job as it doesn't move around.
oh yes I did read about the difference between using tear-away and cut a-way and the results were that it is better to use cut a-way on T-shirts and stretch fabric.
christina , when I embroider say towels I use Sticky back stabilizer and I hoop the stabiler , stick the towel to it and float the WSS on top . Hope this helps . A spring flower for you.
Go down to the bottom of the community page to the very last page, at this posting it was page 102, the last question, "What stabilizers do you use" and I had listed most every fabric and the stabilizer I use. ;)
There are several choices for stabilizing a stretch material. You can use a temporary adhesive spray, water soluable glue stick, sticky paper or just regular cut a-away that you hoop, then pin very well your project or base it to the stabilizer. I'm not sure what fabric you are referring to. After attaching my stabilizer, I try to hoop the project along with it, unless it is velvet or some other type of fabric that will have burn marks. That is where the hoop leaves a permanent mark. I will give you a list that I reference when I am unsure of the type of stabilizer in the continuing post. I have to go find it and copy it. ;)
I use an iron on stabilzer on anything that is stretch. You can get it in tearaway