Ascended Sleepers and Ash Priests reincarnate too, if you ask them about it.
And Corprus was a mode of transmission for divine power. Given enough time, I'm sure that the monsters underneath Red Mountain would have perfected their own control of the disease and become just as formidable as the huge Imperial Legion.
The Ash Ghouls do not say they reincarnate, at least not at the hand of Dagoth Ur.
The soul of Dagoth Gares is among us. You have broken his body, but his spirit is with us in our waking dreams.
As for Ascended Sleepers, what they say is pretty confusing, although it sounds more like the Dreamsleeve.
You think what you do has meaning? You think you slay me, and I am dead? It is just dream and waking, over and over, one appearance after another, nothing real. What you do here means nothing. Why do we waste our breath on you?
But to me, the biggest piece of evidence is that the Ash Vampires, being Heartwights, can be reincarnated, but when they are "killed," Dagoth Ur becomes slightly weakened. But this only occurs with the Ash Vampires.
And either way, only the stronger servants become Ascended Sleepers and Ash Ghouls. Thost that cannon control it degenerate into Corprus beasts.