I can't speak to screening teachers and students (and you may already have considered this idea) but I would encourage you to look at the more culturally-sensitive versions of the ACEs questionnaire and/or the ones that include additional traumas such as "Adverse Community Environments" - these include such experiences as being bullied, experiencing racism, living through a natural disaster, etc. I also think that screening for Resilience factors is important to pair with the ACEs screening so that you can see the a greater picture of the capacities and assets that already exist in your community(school).
We brought info about ACEs, toxic stress, brain science, and building resilience when we did a parent training this year that we called Rise to Resilience. I think it helped us to not just offer the screening, but that background information that we know, such as the traumas they have experienced were not their fault and that while health risk impact can be predicted by knowing our score, it doesn't predict our futures.