I think it's very interesting.
I think the clear retainers might work. I doubt you could facepull with a traditional Hawley retainer though, because it doesn't surround the back molars. The clear retainers do surround the back molars.
You can see, you can use elastics with Invisalign, including class III elastics. Class III elastics pull the top teeth forward pulling against the bottom teeth. The rubberband goes from top-back teeth to the front-bottom teeth. I'm guessing the clear retainers at doityourselfdentalimpressionkit.com are similar to Invisalign trays.
So, if you can use class III elastics, it seems to me that you could use reverse pull headgear (or whatever) to pull the top teeth forward instead of pulling against the bottom teeth.
The question I have is, how could you attach hooks to the clear retainer?