One thing you might want to consider is to see if you can get a few teachers on board voluntarily, for example in the classes he struggles in the most. Even if the school as a whole is opposed to providing formal accommodations such as a 504, I have found that most teachers are very willing to work with students to help them in this area if it’s done in a way that is not overly disruptive or time consuming for the teacher. For example, perhaps a teacher wouldn’t have time to write the assignments down in his book at the end of each class, but if he wrote them down ahead of time and brought the book to the teacher after the bell so as to not disrupt teaching time (or after school or whenever is best for the teacher), then it wouldn’t be too hard for them to quickly look it over and initial it.
If you don’t have any luck with this, keep in mind that the overall goal of this type of tracking system is for your son to develop good habits and skills and find tools that will work for him in the future (when he won’t have you or teachers to double check things). So it is still very beneficial for him to use a tracking system like this book on his own even if you don’t have the teacher’s input.
Parenting Coach, school counselor, author, mom of adult son with ADHD