I have some suggestions that worked for me, hopefully they will help.
I am lucky because my ex just does what I tell him regarding that stuff. He's not too into the "real" parenting, so if I tell him to make sure something is done, he will, as look as he has instructions and direction.
I decided to make my D9 responsible for herself. Maybe a big task for a 9 year old. If she doesn't do the work she needs to at her dad's, it's never her dad I make accountable, I make her accountable. She has a planner, she knows what needs to get done, and if she doesn't do it, I find out. And she gets consequences. Even if I am the enforcer, but the lack of responsibility happens at her dad's.
I would maybe sit down with S8 and explain to him his education is very important and you count on him to be responsible to get his work done and handed in no matter which house he is at. If he knows he is going to a fair, it is his responsibility to make sure his homework is done before he goes.
I know you are trying to handle this without getting Mr. F involved, but perhaps when the teacher reaches out, he should be involved. In a non-threatening open-ended manner, of course. Focusing on your S. Let him know it's great they do things together and enjoy their time together but ask if it's possible to find a time for the work to get done so his teacher is no longer concerned.
My D9 is a tough cookie but also very bright. And a little scatter brained. I expect A's and B's of her because that is her potential. I always get the comment from the teacher "D9 could easily be a straight A student if she stays on task and stops socializing so much" I find knowing that it is HER responsibility and there is no one else to blame but her when she doesn't get anything done motivates her. Especially when there is reward for doing good, or consequence for not.
My ex often rants too about activities and schedules. Which is funny, because I handle it pretty much all. My D9 knows it to.
One last suggestion: Does your D8 have a way to call you or facetime you? Because if my D needs to do something on her dad time, I do call her directly and remind her. I don't know if your ex will see that as an imposition on his time, but if he checked out of the parenting, he may not care.
I knows it's rough being the sole one handling the actual responsibilities. ANd bless you for doing it with 3 kids. One is tough enough for me.
