For the literary problems:

We've already gotten the scene where Harry decides he has something else to do besides killing dementors.

Harry has expressed that he's sure Hermione could learn the True Patronus and wouldn't be able to stop herself from destroying Azkaban. She already has the secret in a note from Harry. She's been introduced to Fawkes. And she was led to her first bullies by flashes of gold and red.

He could have Harry taken to Azkaban, and Hermione break him out. That would be a bit too femi-cliched for my taste, but you never know.

Harry might be off somewhere, and Hermione will need to face the choice of going to Azkaban alone. She might face the choice believing that Harry is dead. EY has referred to Stephen Donaldson before. A "Lord Mhoram's Victory" scenario could fit nicely. (Very moving scene from Donaldson, and perfectly in line with EY's sense of life.) Along that line, maybe all the Dementors besiege Hogwarts (Harry and Dumbledore being elsewhere), slowly wearing down the defenses, and General Sunshine remembers the note from Harry, runs off to get it, and as she overcomes her fear of Dementors and resolves to fight them, she hears a great CAW! and is faced by a phoenix that transports her into the midst of the Dementors and she destroys them all.

I think the groundwork has been laid, and the plot turns aren't so difficult. Hermione as taking McGonagal's in mounting the defense of Hogwarts works for me.