If you are talking to SMT, and this is dependent on how tech savvy your SMT is, they are going to look at the bottom line costs only. They won't care about anything technical, they don't know about your job, won't understand the technical jargon. Won't care that it's complicated for you, they aren't doing it, and your employed to do it.
Think carefully about TCO, and get costs if SW takes care of the hassles by reducing your time on it's monitoring/maintenance, factor that in heavily when you present the figures. The other things you can do:
If there TCO benefits in terms of cost, throw in an additional project you'll be able to achieve, either in total, or sooner than planned, because you're not spending as much time on the current system.
Explain the benefits from a student experience perspective of the new software, emphasising real world benefits. It doesn't matter if they are the same in most part as the current system, however, beneficial differences should go top of he list. If you're asked if they are in the current product, emphasis only those that are additional.
If there are any additional features that you feel are important in safeguarding that the new product has, and the old one doesn't, place major emphasis on those features. Again refer this back to student protection in large and glowing terms.
A three times increase in costs is a tough one though, good luck.