That...is an awesome idea!

I can help out some with developing the world farther, but I don't have time (at least right now) to help with the actual story =/
I'm intrigued by the vines connecting the mats. They would have to be quickly growing vines to keep the mats connected, and they'd have to be extremely strong. I'm also assuming there aren't many, if any structures or buildings on this planet, due to the ever-shifting mats?
Maybe these vines could be like those burrs in the woods, except on a much larger scale. Sort of like natural velcro which would allow a vine to latch on to a mat immediately when it touches it, and then grow around it/solidify that touch.
One more idea and then I'll get off:

What if criminals were launched off of the main network of vines/mats into an unpopulated area with less vegetation - sort of like punishment by isolation?
OK, I lied. I have a question - what about rain? Does it rain here? How would that affect the floating *isn't good at that science stuff*
eru