How do schools view improvement over a student's HS academic career?

Yes, schools definitely do consider upward trend.

Routines and alarms help with ADHD - you have to have a system. I throw things in front of the door so I cannot leave without them, and I set an alarm on the phone to go off at the appropriate reminder time. Maybe he could set an alarm on his phone the night before to remind himself to turn assignments in, that vibrates right as that class begins?