If you know nothing about hosting your own instance why not start learning? Try something slike running Yunohost.org on a VPS and start running Friendica, GotoSocia, Takahe or even ActivityPub on a Wordpress website to get some experience.
If you aren’t technical then you shouldn’t try to make technical arguments but get your academic team to talk to your IT team about the reasons why you want an ActivityPub solution and let them figure out the technical questions.
Wow this is cool. Do you use OpenWrt at all? It would be amazing to integrate with its DYNDns package.