Azazel isn't dead
We have three missing deities, who were all evil - at least, they were by the time they vanished. The Nameless just 'forgot herself' and there's a great big hole where we're told Azazel was thrown. Mah-Nethi, on the other hand, is just...gone. Now, s/he could have just vanished, but all we know about Mah-Nethi's actions suggests an incredibly ambitious and arrogant demon deity, whose works still exert an active force on the Nexus. Such a being would be unlikely to just up and vanish.
Azazel, meanwhile, is the power of Deception. It is entirely possible that whoever threw him through Stygia was deceived one last time, and instead threw a different evil Power...
EVERYONE is a Time Lord
- Everyone in the Nexus has more lives than most people are entitled to. Okay, more than thirteen, but how many Time Lords find that to be an issue anyway?
- Excepting odd circumstances, peoples' appearances only change when they die (except for clothing, which is changed rarely and arbitrarily).
- Time Lords have often seemed more interested in internal conflicts than working on the outside world.
- Not to mention that each of the Doctors themselves are possible physical appearances, at least if you buy them from the shop.