While I found the Black Phoenix curse very interesting, I have some questions. Harry survives a curse which "if performed correctly, there was no surviving." Did Malfoy not perform it correctly? Or do Wizard's not understand it? Naming it after the Phoenix would tell anyone (who knows about the Phoenix) that there would be a rebirth after the burning, wouldn't it? So the name creates an expectation that conflicts with the commentary on the curse. As you have Harry surviving because only Voldemort can kill him (an AU notion), why not simply name the curse the Black Bird Fire Curse? Or, since there doesn't seem to be a bird involved at all, why not simply the Black Fire Curse?
I think this all would have worked much better if the outcome of the curse was unknown (you give that possibility with "few" surviving the second stage) because all the wizards go mad and kill themselves. Then at Harry's burning it could be revealed that the true outcome of the curse to give the Wizard the cycle of the Phoenix (but why "Black"?). So that Harry is made in a sense a Phoenix animagus (or animorph since the change is the result of the curse and not transfiguration).