Oooooo.... A Tyvek hammock. That's one of those projects on my To-do list. I have wondered about Tyvek's weight bearing properties. Be sure to post some pics and give us a report on how that turns out.
I don't know about the whole stove under the hammock thing, but give it s shot if you think it would work. I hope chemically treating the Tyvek won't weaken the material.
“Light thinks it travels faster than anything but it is wrong. No matter how fast light travels, it finds the darkness has always got there first, and is waiting for it."