Serdar, you have very clearly described and diagrammed the prevailing problematic forces at play, and your proposal is taking shape in a very promising way. Fine work. One key point I see is your pitch for the schools to be solar power stations: is this a short-term or long-term proposition? Since you need the generator before you can begin providing juice to the batteries, how soon would that be achieved, and at what related costs? What systems/examples exist that you can reference (check with your nfp), or are you proposing something new? One key suggestion is that you might take a cue from Oz's human-powered energy ideas to provide a "jump-start" to your program. How many ways could you harness childrens' exuberance with context-sensitive materials and costs? This could be a temporary solution, or one that expands into the home, from the school.
Also, will you be developing your lamp, too (with mechanicals, prototype, etc.)? Keep going, you're on a good trail!