Ye gods, I've done it.
I was messing around, and I do believe I have what we need.
I mixed some nail hole filler (spackling) and cyanocrylate. It dried quickly, and was very fragile. I mixed then Cyanocrylate, spackling, spirit gum, and water. Very strong, but not elastic enough.
Finally, I mixed spackling, Cyanocrylate, spirit gum, soap, denatured alcohol, a little soap, and some Liquid Plumr. I was able to stretch this to over 20 times it's original length. I made a big bowl of it, then pulled out a strip of it and stuck it to a wall. My 200 pound brother grabbed onto it, leaned back, and leaned back almost to the ground. It didn't break.
There is no telling what this stuff could do after being put through a spinneret.