You could do the envelope and tie it but if it is really stretchy, it may still be difficult. Are you using a flat sheet on the back with no batting? If so, I think I would lay it out flat on the floor and tie it.
When tying, place a marble under the backing so you can roll it around so the curved needle has room to go through and come back up. Once stabilized with the ties every 4 inches, you could then put a binding on.