I would say all of them.  However, if we are going to do Hortator quests, shouldn’t we follow the pattern set by vanilla, in which the player does one of the final quests for the faction?  If so, we need to have established those first don’t we?

Honestly, this is one of the topics I don’t feel terribly invested in, but that doesn’t mean I can’t write a large post about it nonetheless.

The straightforward approach I’d considered for Indoril before is that they would formally and automatically recognize the PC as Hortator after the PC meets with Vivec, which assumes this bit doesn’t need to be done in chronological order:

I don’t think I had any idea on Dres back then. In general, TF’s majority vote idea would work quite well. That being said, I think both are certainly cop-outs from a narrative standpoint. One asks the question: why does only the majority need to recognize the PC? And the answers are either ‘Indoril and Dres wouldn’t accept an outlander Hortator’, which I think rather lacks imagination, or ‘we don’t want to mess with vanilla content’, which has nothing to do with the narrative.
On the latter point, there has been some discussion on how much would actually need to be changed. One specific suggestion was to just leave out the ‘three Houses’ and ‘four tribes’ lines from the above cinematic, which are arguably a bit redundant to start with.

As we have characterized House Dres – certainly as I’ve characterized them in my WIP questline – there’s one straightforward way to get recognized as Hortator by them: buy their recognition. Trade them something they perceive as equal value. The issue being Hortator is an incredibly valuable title, and the PC, as an outlander, lacks worth. The latter point can be amended in three ways: the PC proves their worth, someone with preestablished worth carries out the transaction in the PC’s stead, or the thing being offered in return is just that valuable to the Dres that being offered by an outlander does not sink its value enough to stop it being worthwhile. If we follow the vanilla model, the PC would need to make separate deals with all the Matriarchs, I guess.
With Indoril, things are less straightforward, but not for want of possibilities. I think Temple approval is not really the best approach as we’ve characterized Indoril, as illustrated by the Armistice: just because the Indoril don’t go against the Temple doesn’t mean they agree or accept all Temple decisions. That being said, Indoril Nerevar Mora cheated and lied his way into the House, so that’s one valid and narratively fitting approach for the PC to get Indoril approval. The other approach that springs to mind is a legal argument: for instance – presenting the case in such a way as to not immediately get reported to the Temple for heresy – making and winning a case demonstrating link-via-reincarnation to Indoril Nerevar.
Basically the Indoril, while not obsessed with law as such, operate through administration. They tend to focus on technicalities and place things into neat categories. The PC just needs to mess with their categorization and get ‘misplaced’. To become part of and justify their worldview rather than being an anomaly to be removed.

Having established that – at least in my eyes – acceptance as Hortator by all the Houses would be viable, I do actually have some narrative arguments that might speak against that approach:
While we make it pretty clear there are specifically five Great Houses, and they are organized in a council (often halfheartedly) and so on, things get murkier with the Ashlanders. I don’t see why the Ashlanders would have such a clear divide between their tribal camps and smaller camps. Especially on the mainland, the tribes have enough trouble keeping track of their own members, let alone each other. I don’t think getting the recognition of ‘all the tribes’ is a clear enough objective, basically.
The natural alternative, then, would be numerology. Pick a number that has significance which does not exceed the total number of tribal camps we will have in-game. Upping the Houses from three to five already broke the four-three/seven numerology (aha, another argument for the majority approach). Seven tribal camps would be the natural solution, but if the Ashlanders are the good and bad Daedra, what is the significance of the number five beyond simply ‘the Houses’? The corners of the world?
And the final issue is pacing. In vanilla Morrowind, you need to convince four Ashkhans and all the councillors of three Houses to accept you in one specific stage of the questline. In the case of TR, there would be more Ashkhans, more councillors and Houses, and far, far more ground to cover. That stage of the questline would be given a far greater role than it currently has, and might disrupt the pace of the questline as a whole. Which is not necessarily a bad thing, but seems like it needs to be a conscious decision; if we want to roll with that, I think we may need to make more significant changes to the Vvardenfell Hortator and perhaps Nerevarine quests to match the new context.

To round off, I will say the ‘three Houses on Vvardenfell’ idea seems very flimsy, again from a narrative standpoint, and I doubt we would be well-served copying the vanilla pattern of overlap with the final Great House faction quests and getting recognized as Hortator. That is one vanilla convention we will disrupt either way by changing who the councillors of Telvanni and Hlaalu (not Redoran as far as I can recall) are. Our narrative approach is a bit more focused in direction than Bethesda’s, so I don’t think the last few TR Great House faction quests will be as easily torn from their contexts as their vanilla equivalents were.

Practical me says the first option, because it’d be a massive undertaking and we need to finish TR first.

Idealistic me says YES DO IT NAO ALL THE HOUSES! ...and the tribes too!

#3

In my mind, the Dres Hortator quests should be centered around the Satchim-Ichil and not scratch deep underneath the Dres surface. Understanding the Dres secrets is not something a war leader needs to do, they just need to lead their troops.

A good precondition would be to be Hortator of at least two other houses.
A couple of quests to convince the migratory council that the player is the real deal, one questline that resolves a minor pact of a Matriarch (like carrying a magic doodat filled with blood to a sealed Daedric ruin), one masked figure sniffing out the Nerevarine’s soul while they’re in a drug-induced haze according to “ash baptism” or some other made up ceremony, done.

Indoril I see pretty much like the vanilla questlines.

There’s also the question of the mainland Redoran/Hlaalu/Telvanni councilors. They should have their own little quests similar to the VV ones when we unify the factions.