If you only need a place to perform, there is a stage in the cafe in center camp.
You could ask to be on the schedule.
Anyone that has a space you could perform in, has only to agree to let you do it.
If you want to set up your own space on the playa, you have to be placed by the art folks.
Or you could set up a theme camp to perform in.
Otherwise you just make the arrangements to perform where you choose.
http://www.burningman.com/on_the_playa/ ... /cafe.html
I like the direction you're going in.
I've played with some similar ideas for static pieces, reflected images layered on another image.