This is absurd: You thought up a detailed scenario, and you assign it ten times more probability than all other alternative scenarios of apologies put together:
- Harry apologizes in person
- Harry apologizes in writing (but without making a list of people versus Galleons)
- Harry apologizes through an intermediary (e.g. "Professor McGonaggal, please tell the Headmaster I'm sorry for the things I said", or "Fawkes, give Albus a hug for me.")
- Harry apologizes indirectly by defending Dumbledore's actions in public to Hermione's classmates.
- Harry apologizes through an elaborate prank that utilizes the Time Turner, the True Cloak of Invisibility, and exploding birthday cake.

Etc, etc...