The sudden knowledge that the Tribunal were false gods, thieves of godly power and possibly murderers of Nerevar should've brought total obliteration to the Temple and its members. Maybe Helseth & the Dissident Priests realized this, and never made it public knowledge, but instead made it be known that the Tribunal finally ceased to be man-gods and ascended for ever, or something.
This conclusion generally rules out simple denial. I'm not sure if the future beliefs of Morrowind Dunmer are focused on after Morrowind, but you have to consider that the Tribunal have been worshipped for over a thousand years. They are gods, they don't die. Or so the Temple-abiding Dunmer believed.
For instance, try walking up to a devoutly christian person and saying "Your beliefs are untrue, Jesus never existed." Will they believe it? Probably not. Now, suffice to say, when the Nerevarine Prophecies and their outcomes are effectively rubbed in the nose of Temple priests and citizens, you'll have a religious dilemma --possibly comedic, possibly horrendously violent-- that could destablilize what little and seperated order that is loosely knitted together in Morrowind.
And, concerning your statement about the Tribunal even 'ascending' to Aurbis or Aetherius, could be met with less-than-open arms. Given the aforementioned period of the Tribunal's (Blessed Be Their Holy Names) reign. As far as Templegoers are concerned, the Tribunal are 'The Gods,' all other et'Ada have the right to bow down to these divine pretenders. The Temple would never admit to their Gods' losing divinity, given the said statement about them being > the Aedra, Daedra, and all et'Ada.
The rumors of the Nerevarine's trip to Akavir could be a completely fabricated cover-up for something more sinister. It's possible that the Temple implemented a more diabolical solution to these radical changes in an attempt to quell the crisis (assuming they could lay their hands on his game-mechanically invulnerable self.)
Considering these rumors (given what's possible in-game,) began while Kvatch was still under siege and the real 'crisis' had yet to begin, it's possible that without a Hortator or Nerevarine that Morrowind could be obliterated by unfathomable instability and Daedric splodey-machines.
Edited for saying the word 'sinister' twice in one paragraph