So I'm having trouble understanding all of the different accounts of what happened on Red Mountain.

The Tribunal says that the Dunmer fought the Dwemer, that Dagoth Ur was corrupted while guarding the heart, and that Tribunal avenged Nerevar's death and only acted wrongly later when they used the Heart.

The Nerevarine Cult says that the Dunmer fought the Dwemer, that the Tribunal betrayed/killed Nerevar, and that Dagoth Ur also betrayed him.

If that's as far as you go then there isn't TOO much controversy. You can pick your story or something in the middle. I tend to lean towards the Nerevarine story and view the Tribunal story as a cover up. But then you get this third version from Wulfharth...

The Five Songs of King Wulfharth says that the Battle of Red Mountain was NOT fought between the Dunmer and the Dwemer, but rather by the Dunmer and the Dwemer together as a united force against the invading Nords. In this version, both the Tribunal and Dagoth-Ur betrayed Nerevar, the Dewemer, and the rest of the Dunmer prior to the battle even happening. Wulfharth claims that the Tribunal sent Dagoth-Ur to tell the Nords where the heart of Shor was. Then, the Nords and Wulfarth invaded against a united force of mer. Dagoth-Ur struck down Dumac Dwarfking, Nerevar struck down Dagoth-Ur, Lorkhan mortally wounded Nerevar, and Nerevar struck down Lorkhan before he could fully reform.

What doesn't make sense about this version is that the other versions don't even mention the Nords being there. Why would the Nordic invasion be kept fully out of the Tribunal version, the Ashlander version, and Dagoth-Ur's version? I have a few possible answers:

1) Wulfharth is a liar. As an aspect of Lorkhan, he is a trickster. Telling a story in which Dagoth-Ur and the Tribunal betrayed Nerevar and the Dunmer would be a good way to discredit the now divine Tribunal in the eyes of their people and people across the world. Wulfharth's story could be interpreted as the Tribunal and Dagoth conspiring to gain acess to the Heart at the expense of their people and all morality. I actually like this version because if Wulfharth is a liar I can discredit the Arcturian Heresy. It could be that Wulfharth wants to discredit Talos or at least take some of the glory for himself. Maybe he's jealous that Talos was a more successful Shezarrine than himself as he finally returned Lorkhan to prominence.

2) There was a Dragonbreak. This might seem like a bit of a cop out at first but it actually makes sense. If the use of the mantella (a much weaker version of the Heart) could cause a Dragonbreak, then the use of the actual Hear could do it for sure. If this were true then all sense of time and space became obscured during the battle. Several contradictory events happened all at the same time and were experienced differently by different people. Only the outcome would be certain.

3) Wulfharth's version is true. This is especially appealing if you accept the Arcturian Heresy. Maybe the reason neither Dagoth nor the Tribunal mention the Nords is because it would make them both look bad if the Dunmer knew they brought on a Nordic invasion force.

Any other theories? Which of mine works best?

I'm not sure if a dragon break occurred, but one thing is clear as suggested by the account in the Five Songs (at least to me): the battle at Red Mountain is a microcosm of the Dawn. In response to your third hypothesis: Wulfharth's account is true. They all are. Wulfharth's impassioned queries to his men (“Don't you see where you really are? Don't you know who Shor really is? Don't you know what this war is?”) reinforce this idea.

The confusion between things like the loyalty of Dagoth, presence of the Tribunal (and Shor), and allegiance between the three parties mirrors the dawn perfectly. It's different from each angle. At least this is how I understand it from some talk on past discussions. Someone else will be able to summarize it better.

There was a Dragonbreak at Red Mountain when Kagrenac activated the Numidium.

When the Dragon Breaks, time shatters into more times or rather, they can split.
So all accounts can be true, and at the same time be untrue.

That's what the Jills are for. To mend time.

A Dragon Break occurred when Kagrenac used the Numidium and destroyed his people or sacrificed.
A Dragon Break happened at the events of Daggerfall when Mannimarco the Psijic, became the Necromancers Moon, and himself. And so on.