In short, you can't do what your trying to do.
Atleast not with this router and the software you have at hand. The whole point a proxy server is set up at your campus is for security reasons, both for you and them. Since your signing in with your account info, your saying "this traffic is from me". That lets them track down security threats, and also manage bandwidth.
Your best bet is to contact who ever supports your network. Maybe start with student affairs? Or look on that proxy sign in page for a "Help" or "support" link. Depending on what kind of proxy they use, what kind of provisioning software, and their network terms of service, they might be able to add the MAC address of your router to their system so it doesn't require a sign in. I would give your chances 50/50.
You could still maybe get a AP, and then find some kind of App or setting in the phones to configure the proxy. That might be a work around.