Optimizing a website for School Networks

We are a nonprofit which is building an online mentoring platform that is designed for students. A big problem that we have been running into is that our site sometimes behaves differently inside school networks than it does anywhere else. We've been able to clear up some issues by asking schools to adjust their firewalls, but I am looking for a more consistent solution.

I was wondering if anybody could offer me some insight on the best way to optimize our website so that it will work inside most school networks. Are there standards that districts follow when setting up their network and computers? Are there key things we should ask about changing? Anything I should look for when testing?

Our organization is called EduGuide, and our website is at http://www.eduguide.org. Feel free to check it out and let me know if you need more information or can help out. I can be reached at jon@eduguide.org. Thanks.