Hi William,
"What about weaving or sort of crocheting strips/foam yarn? How about just a loose weave wool garmet? I guess that's the old historical model people have been referring to. I've got a blanket my mom knitted me draped over my shoulders as I write this. Depending on your pattern I think you could make something pretty strong. I'm thinking of a very loose weave to create lots of air space."
I have no idea about your first question. Foams don't have much tensile strength in general, but if you could find tubular strips of evazote foam it might work being more flexible, elastic and tough compared to a lot of other foams.
Loose weave wool garment is an ok model, but wool is relatively heavy, takes awhile to dry, and gets rather weak when wet.
Some companies, like the Scandinavian Byrjne one i mentioned much earlier here, make fishnet wool garments. I don't have any experience with the wool version, just the polypropylene one, but some people seem to like them a lot, and it's very similar to your proposed idea.
What would be really awesome is a polygiene treated version of a Byrjne polypropylene fishnet shirt, if it was reasonably priced. Polyproplyne is very light, fairly strong and tough in woven forms, and absorbs very little moisture. Problem is it can stink to high heaven, and that line of clothing is generally fairly expensive. I got mine on clearance.