What a charming, engaging, fascinating story! I loved Prospero right from the get go, but thought it might just be the team rivalry rearing its head. When it turned out that it was Harry, I was intrigued!
I loved the name, as the Tempest is my favorite Shakespeare of all time. His love of the library was perfect - "Library was Dukedom large enough" -and his affection for Dumbledore seemed rather like a parent/child, even though they were reversed. His command of magic was so elemental that again he mirrored Prospero, and in the end, he again chose Prospero's road. "Yet with my nobler reason 'gainst my fury/ Do I take part. The rarer action is/In virtue than in vengeance."
This also reminded me of a wonderful series by Naomi Novik: The Temeraire Series. (I think there's also an active fanfiction community that the author encourages, as she was a fan fic writer herself.) The wisdom of the dragon, and the misplaced dragon, far away from his home, had the feel of Temeraire, and Capt. William Laurence finding himself suddenly with a dragon was rather like Snape. I'd highly recommend it, if you haven't read it. And of course, I loved the dwarves, which seemed a nice tribute to LotR.
Your work evoked these stories in me, but was never derivative. Instead, it only did it in the general, familiar way of any great story; the moment where your heart warms to the characters and tale, and you settle in, knowing you will be satisfied. This was a story I'd like to read over and over and over again.
Thank you for sharing it! I can't wait to start it all over, and find other stories of yours to enjoy.