Actually OP, I think you’ve possibly done your DD a disservice by describing this as a timekeeping issue.
Yes, timekeeping is hard with ADHD but yes, you do have to learn how to be on time (even if it’s just skidding through the door on time by the skin of your teeth 😂).
However what you’re describing here is actually a sensory overwhelm issue, not organisation or timekeeping. The lateness is the net result, not the problem.
Your DD is actively hiding elsewhere to avoid the noise and crowds because she can’t manage. And then because of that, she’s late.
Talking about time management and neurodivergence on MN is like a red rag to a bull - I’m not reading the thread as I saw it was full of the usual dickish comments. I’m not wasting my energy. I read your comments OP.
Obviously this pattern at school isn’t sustainable, especially as your DD is starting to become a school refuser.
You either:
Home educate
Switch schools - are there any without a waiting list other than the other one you like? Parents may prioritise schools with good exam results but what you need is a school that’s good with SEN; they’re not always the popular ones
Write a letter of complaint to the governors based on the advice you’ve had here (I saw some helpful comments early on - I’m sure there are others mentioning need not diagnosis/SEN code)
You say the school isn’t amenable to options like letting her out a minute early, wearing loop earbuds etc, so I’m not sure what else you can do? The longer it carries on, the worse this is going to become. Sadly, from experience, schools are either good with accommodating SEN or else they never will be. And if they’re the latter, you really are better off cutting your losses and getting out of there asap - even if you home educate for a while.