Hi Ange, I think you have a great idea here. I found one additional reference that might bear looking into: http://empowerplaygrounds.org/ Their company mission sounds similar to what you're trying to accomplish.
Also, I love the idea that the first piece of playground equipment that you install helps to fund the second, the third, etc. I'm wondering if you could take that further to give the idea more of an incremental approach; so it wouldn't require as much up front investment to get started. Instead of having a university design a whole park, could you start with just a single piece of playground equipment? Possibly approach an engineering professor, and have them offer a course where the students collaborate to build a single piece of energy-generating playground equipment in their community. Then, if that is successful the university could build on it the next year, and so on and so on. By gradually proving the idea you could gain acceptance, prove the idea, and generate funding for the next iteration.