Hmm here's a crazy idea! I've made structures in the tropics before by propagating living plants that grow like crazy in that environment, kind of like this: http://inhabitat.com/diy-bio-tecture-build-your-own-backyard-living-willow-dome/ or this http://www.apieceofrainbow.com/10-amazing-living-structures/
I can't remember the names of the plants we were using though.
You could potentially do the same for a low cost and beautiful shade structure that you could plant inside of, that way the plants are protected from too much sun and heavy rain.