If it’s per university, see if you can have someone Venmo you a few months worth of subscription (to prove the model) before worrying about anything else. But it’s gonna be hard to make a living at this price point. Consider raising your price by 100x and see if they still love it then.
If it’s per user, see if it works for non-universities. If you can, let them use it for free, get a case study and go sell to every other industry, they will all be easier. We started our SaaS in a similar way at a lower price ($5/user/month), 10 years on we’re still rolling and we have never charged our uni a dollar. Feel free to email me if you want any more advice on this.
(Not a lawyer.)
ps. What does your app do?