I would first consult the lead teacher in the classroom. Student information is available on a need-to-know basis, so if they are willing to share IEP information with you that could assist in strategizing how to make transitions smoother, that's where I would start. ESE students are often triggered by transition times if they are focused on the activity that is taking place. I would suggest you try having calming music playing during activities and have a visual timer on the board to signal that it is time to transition so that students are aware of the time limit and can prepare themselves for the transition. This will also build their time-management skills. Another suggestion I have would be to use the assertive approach rather than a stern approach. As you noted above, a stern voice only helps sometimes. The assertive approach ensures that you are not damaging the relationships you have with your students while also maintaining the teacher-student boundaries, thus allowing you to maintain control. Using positive behavior incentives and praising students who remain calm during transition times could also be used to model the behavior you want to see in the whole class.

I think that starting off the class with an activity that can let the students get all of their energy out may be beneficial. Once this is over start with your lesson and see if this helps!

A lot of ESE students actually need to get this energy out in order to be able to focus on the material at hand. I would look into if your school has a movement or sensory room and see if students would benefit from 5 minute breaks there when they feel the need to move.

You've got this!