As discussed before, this is a nice idea. The self-funding thing would be hard but I'm pretty sure we can get gymkhana funding.
There was once a similar competition at BITS (restricted to BITS students, but I didn't know that and participated online anyway :P) though it was more on the usual CTF format (solve a challenge to unlock the next one). Questions and solutions can be found in
this blog post I wrote. Ideas can be taken from there. Aside from that, Security Stack Exchange has a CTF team that's semi-active. We post solutions on the meta once the CTF closes (see
here), you might be able to pick up some questions there though most of them are a bit advanced.
I don't mind helping but I won't have the time to sit and code this :P