Generally speaking, I like the idea of Morrowind being a stable and non-expanding blob, so the point is, in my opinion, to make the kingdom inner intrigues and war the focus. Although I agree mostly with what Tingyum has said, I'll expand my own point of view.
DISCLAIMER: All these are just ideas, nothing more. I don't really know if it's easy or difficult to do, and of course I don't expect everyone here to think they're good ideas at all. They're all just my own opinion, and I'm just trying to be helpful to the team.
1 - Custom goverment: Morrowind is not a kingdom proper, with Almsivi as their three god kings and the Grand Council as their, so to say, "secular" government. This custom government should be related to Almsivi religion to represent the covenant between the traditional dunmeri houses and the Tribunal, and it should be always elective, to represent the power struggles between houses. Elections should not be tied to ruler themselves, but rather by the influence of the great house you represent inside the Council. I know, for a fact, that custom made events that simulate some kind of elections and/or rulership change related to other factors are possible, so it would be a great addition, in my opinion.
2 - Great Houses: Great Houses should be one of the main focuses of the overall change to Morrowind. First of all, as it has been said already on this forum, the whole induction system should be introduced, and of course expelling someone from the house, even if difficult, should be a possibility. Moreover, being a member of a house should be something more than simply having good relationships with other members of your house. I don't really know if it is possible and even desirable for most players (for me, it is), but I'd like to see a house council system in which dunmeri councillors struggle for power as well. I don't know the proper way to do it, but to prevent the whole great house system being linked to titles that come and go in a weird manner I would make a titular duchy title, similar to religious title, with no vassals, not creatable and representing the current head of the house. Having this title should give some new diplomatic actions representing the power of the current head of the house, like expelling members (should have downsides) and trying to change current councillors (may be a trait or an effect tied to the House trait) so they're more loyal. I'd also add a kind of negative effect, similar to republics, for not having a councillor as a member of your government. Concerning the Great House leadership, I thought of two distinct systems: one should be pretty straightforward and simple, with the title being inherited with a normal primogeniture but with an event chain leading to a change if your councillors are disloyal; the other one could have some elective system tied to all the members of the house, although it can be difficult to implement and play. With each system, anyway, players not being the current head should have some kind of distinct possibility, intrigue or event related, to try to become the current head of the house.
On a separate issue, just to make it more "realistic", I'd like to see great houses more related to their traditional theme: Telvanni having wizard/priest educations, Redoran with barbarian/knight/warrior, Hlaalu with business or stewardship, Indoril with priest/knight and Dres... well, I have no idea with Dres, to be honest. This is not really something important, but if implemented would make Morrowind more consistent and could be even important for Great House leadership as well (it's not the same being a Telvanni Master Mage than a simple Telvanni clumsy trickster if you want to become Archmagister). Also, just for flavour as well, each Great House title could have its own localization, with Telvanni being Archmagister, and so on.
3 - Grand Council: The Grand Council would be made by the heads of the five great houses, with one of them "being", in Ck2 mechanics, the "king" of Morrowind. Being head of the Grand Council would have some pretty obvious advantages (all kingdom mechanics), but it should be somewhat limited to represent the whole idea of Morrowind not being a proper kingdom, ruled by a very independent nobility. As such, crown and normal laws should be somewhat limited and tied to the custom government I mentioned. The Grand Council should, more or less, work like the Great Houses but without single members of each house having anything to say, just the councillors, which are each Great House head. Of course they will expect to be in the council (maybe not the Telvanni : P).
About the way the great council head is elected, and Morrowind inner politics, I really have a lot of messy ideas. The whole thing should revolve around the "influence" of each house inside Morrowind. Influence should be, more or less, the amount of lands held by a house as a whole, the Great House head (wealth, attributes, prestige, favour), and miscellaneous factors. With enough "influence" (support, whatever), the head of a house could try to enact a decision to challenge the current leadership of the council, with some degree of randomness so it isn't a certainty (like and intrigue, so to speak). The miscellaneous ways to gain could include House Wars (explained below), as well as any other things that people may propose.
Just for flavour, and for players who want to change history (CK2 is about that, after all), a very difficult decision could be made to allow the player to form a normal kingdom of Morrowind, destroying the great houses and challenging the traditional ways of the dunmer, but that would, of course, require the Tribunal's approval, which can be tricky. Otherwise you should end with your kingdom being invaded by Vivec, Almalexia and Sotha Sil. Other conditions could include destroying other houses, becoming the only house with lands and such.
About how influence is measured, I have no idea, to be honest. Maybe a hidden variable should do the trick. Anyway, a house with a massive amount of influence over the council should enact some kind of reaction from the other houses, trying to retain the balance, and may even lead to a civil war.
4 - House Wars: This should be, in my opinion, the main way to change the influence, but it has a big problem: CK2 is a game about war and intrigue, but war if definitely fun. Problem is, the Tribunal banned wars inside Morrowind (proper wars, at least), so there are two ways to handle this issue: canon way and non-canon way.
4.1 - Canon House Wars: Morrowind custom government should have a form of internal king's peace that cannot be removed unless you change the whole government. Therefore, the only way to do house wars and expand your territory should be intrigues. That would require a lot of new intrigues (involving the Morag Tong, of course), and some of them would simply modify influence/prestige of two enemy houses, while others could be use to take lands you have a claim for.
4.2. - Non-canon House Wars: More or less the same, but instead you could simply declare war to take lands (traditional CK2 way) and may even have some kind of "house war" CB to just crush an enemy house, gaining wealth, prestige and/or influence.
My personal take is for Canon House Wars, but I know it can be tricky and even boring to some players, because the whole warfare thing is almost abolished if you go that way.
5 - Religion: Religion is of paramount importance in Morrowind, compared to other regions. This should be definitely something to take into account when making any changes. The Tribunal itself, and the Almsivi "church", should play a more critical role in Morrowind as a whole, challenging rulers who do not fit the Tribunal plans (again, with single events and event chains as well), representing the "real" authority of Morrowind. For example, a necromancer ruler of the Council should be allowed, as with Meridia, to renounce his evil practices or be branded a heretic. A more simple and less heavy-scripting approach could simply add requests and/or missions that give or take Favour from rulers. Also, having a high favour and being loyal to the values represented by the Tribunal could give some boosts or penalties. I would add, as well, the possibility to have a "patron" god like with Eight Divines religion. As much as the dunmeri people worship their three gods, having the possibility to choose your "patron" would add some flavour as well. Redoran would surely worship Vivec with a lot of enthusiasm, while Telvanni wizards would revere (if they were into the "worshipping" thing, anyway) Sotha Sil; Dres and Indoril traditionalists are more tied to Almalexia, for example. Hlaalu care only for money : P.
6 - Vvardenfell: Vvardenfell is a sacred island for the most of the second era, with just a bunch of ashlanders tribes warring the Tribunal. What we see in TES III Morrowind is the result of Vvardenfell being colonised (there were settlements before, but too small and unrelated that are almost of no importance). My personal take would be to turn Vvardenfell in a place full of small tribes of ashlanders using HL mechanics, except Vivec and Sadrith Mora. Any attempt to invade, colonise or do whatever you want to do against Vvardenfell tribes would anger the Tribunal, which would require you to stop, because Vvardenfell is a sacred place. After an event related to Dagoth Ur and/or the Empire conquest of Morrowind, the Tribunal could let people to colonise Vvardenfell (as an event, or maybe a law proposed by the Grand Council), slowly becoming part of the kingdom gameplay wise.
I know using things from DLCs is something the devs try to avoid so everyone can play the mod without issue, but if HL mechanics are not desirable, plain tribes will do the trick as well. The main point is, anyway, turning Vvardenfell into a empty place awaiting to be colonised in a later date.
7 - Nerevarine: It has already been said, but the whole thing on the Nerevarine Cult, Dagoth Ur and the Reclamations would be great additions. My take on it is very simple: Dagoth Ur becoming more powerful was a matter of time, as we learn in TES III. Therefore an event chain should be triggered radomly, but with increasing chances as the game advances. Once Dagoth Ur awakens and challenges the Tribunal, their event troops should be largely diminished or completely removed, to represent Morrowind having to fend for themselves without their gods. Then, the whole nereverine plot should start. There are two ways to do this: historical advance or player meddling. The first way should make the raise of the real nerevarine a matter of time, and only an event, leading to the Tribunal end and the Reclamations becoming the new religion for the dunmer and ashlanders alike (This could, in turn, make it easier to change Morrowind into a different goverment, as you no longer have three god kings watching you). The second way could include, as with the dragonborn trait, a nerevarine trait to become available to a random character. This character would in turn have some events to fulfil the prophecies (you, as a player, may decide to help or hinder his advancement if you are anywhere near Morrowind/Vvardenfell or have him in your court/realm). If he fails and/or dies, it's a failed incarnate; if he manages to fulfil them, then the whole Reclamations events fire.
EDIT: The Nerevarine should be lowborn (uncertain parents, prisoner) and unlanded (sadly, no player nerevarine : P). That is, if we just accept the canon as is. It's up for people to decide.
8 - The fall of the Great Council: Should the Great Council cease to exist because of an invading force (The Empire, the Kamal, whatever), and not because a reformed kingdom of Morrowind arose after one house managed to be the preeminent one, the Great Houses would continue to exist, but their relationship to the king should be completely different. To make things easier, they would just become normal vassals, and will be subject to the laws of the new country, but with enough support and military might a house or alliance of houses could try to start a civil war to create the Grand Council again.
And that's it. As I've already said, but just in case, I do not expect all of this to happen, I accept constructive criticism and I apologise to the devs for not being a scripter, just giving ideas without actually making them real.