I’ve been through the university procurement process. My experience wasn’t too bad. There’s a bit of red tape but the folks who want your solution are probably willing to minimize the process as much as they can (though you’ll still need to complete it).

I would also consider charging for non recurring engineering fees (sort of like consulting).

Instead of $16/mo/user charge a few thousand $s for integration or custom development. Paying for labor is something companies understand very well.