This is really lovely, on a number of levels. I like the period setting, and the details of magical and mundane life that bring it to life. I *love* Prospero, and while I figured out pretty quickly who he 'really' was, that knowledge didn't in any way detract from my enjoyment of the story, or from the fun of waiting to see how long it would take Severus to figure it out. Severus himself was lovely, still sharp-tongued and prickly-natured, but without the bitterness and self-loathing engendered in him by canon events, and I enjoyed his interactions with both Prospero and Harry, and how those relationships deepened as the story went on.
Your Dumbledore is very canon-like in his . . . what? well-meaning manipulativeness? It's like he would *like* to do the best for others, but he can't quite bring himself not to twist them around for his own ends.
The Dragon/Phoenix mythology was rich and intriguing, and I like the idea of Harry as a future teacher of Dragon descendants. Of course, I also like the idea of Draco (heh!) *raising* Dragon descendants.