Best process for excluding non-relevant college and university personas from targeting?

Several of my company's product offerings align well with colleges and universities, however, we have a hard time targeting the key decision makers due to students and other non-relevant personas eating up ad spend and showing false positive signs of intent.

I've tried narrowing down persona targeting in campaigns, but it is difficult due to current students being Presidents/Leaders of student orgs, past students that have graduated but are still being affiliated with the university in the data, Masters students previous positions muddying the data, etc.

Additionally, due to the nature of my company's products, we receive a lot of false positive signals from students conducting research and hitting our generic keywords. I of course do not want to remove these keywords from our model in the scenario that we would miss true intent signals.

I also do not want to fully exclude education industry accounts from our campaigns/segments since they do align with some of our offerings. Has anyone else dealt with colleges/universities interfering with their data, and found any work arounds/best practices?