None of my business, don't mean to rain on your parade, but here are some thoughts:
Access to dome:IF you build this, whatever access you have for yourself, your camp, to run and maintain whatever is going on inside the dome... you most likely will have a direct entrance....this entrance will be figured out by the masses and they will not use the spiral. As a kid, in the house of mirrors, all one had to do was look at the floor to see where people had walked. I believe most burners are not the type to bump into the mirror.
"Stretch fabric" if you are talking Lycra, have you priced it? I bought a 6' wide 100' long bolt of Lycra to surround the bottom portion of my dome (which I designed specifically for the stretched out lycra.) I think it cost $600, and yes, it still costs the same
http://www.stretchhouse.com/nylonspandex.htm#Regular Spandex . (better copy and paste the link). It looks like your spiral would consume at least 400 feet of material, much more if not just walls, but covered on top.
Side note for attaching line to any fabric:For all fabrics in uses like shade, use use marbles and pieces of strong small diameter rope, tying a clove hitch around the fabric that is covering the marble. Much better than gromets that can fail when they cut the material...also, the gromet doesn't distribute the stress as well as the "bunched" fabric. The marble and rope method is what's holding the stressed lycra on the dome: (sorry, pic link long gone)
Any material in the windBut especially lycra, will be windcatchers. On a dome, windcatchers are one thing as the support system is solid. But in your spiral, I would imagine a disaster in strong winds unless the support system is very costly.
Time needed:Your camp will probably spend more time on the spiral than the actual dome. Whatever system you use, it will probably not be tested beforehand and problems will evolve that will be unsolvable or consume so much time many will feel their playa time wasted, as what was thought to be a one day project stretches to three, and then the thought comes up "Why finish, there are only a few days left here!"
I always am amused to see incredibly ambitious projects being worked on feverishly for a day or two or three, then abandoned. I'm amused as it is heartbreaking, as I've been there, but the positive aspect is that those involved will certainly learn to scale into any new project understanding that the playa is not giving you any extra time/resources/labor hours to work things out.