Hey JM, glad to hear things are going well with the new lady!
Try not to get angry about W proposing a new schedule, you're legally divorced and she can't just change a documented schedule without your buy-in. You can simply say "no". You don't like her proposal and she doesn't like yours, so both of you are left with the current court-approved schedule so there you go. Not sure why she thinks a mediator would touch a court-agreed schedule, I find that highly unlikely.
My ex and I have a weekly split and that has worked well for us. The two girls are grown now so it's just S15 that is subject to it. He NEVER EVER is late on my weeks. I mean literally, he has not been late once in all these years we've been doing this. When my ex has him he's late pretty much at least once every week she has him. It's aggravating, but at least she doesn't blame it on our schedule.
EDIT TO ADD- my S actually told me he lied to ex about what time he needs to be at school! He told her 15 minutes earlier than the actual time in the hopes that she would get him there on time. As a result she's managed to get him there on time more often this year although there have still been some slip-ups.