I'm not saying its not worth a try, actually I'd love to see it be a success. I'm just pointing out some potential shortcomings of the concept, won't know til ya try I guess.
Seems like Canoebie has some wool fabric that they take, used mostly as a blanket or to lay on inside the hammock, but I think he said it was suit lining material made of wool, so it was thin and light. Might be worth a look at Joann Fabrics to see what they have.
You could try felting it too to tighten up the weave maybe??