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Morag Tong like Dark Brotherhood or Shadowscales should be in my opinion from some DLC a playable faction, with seperate skill line and / or daily quests.
The guild is so rooted in lore I simply cannot imagine otherwise.

Mechanic:
It is possible to implement this guild respecting the lore - it's actually very simple. It can works like vampires and werewolves. Both factions have their quests and skills, but to join one, you must leave another. In ESO we have recently so many content we could implement such a rule without risking the lack of availible amount of playable adventures in the world.

Lore:
Oh, gosh, how many possibilities

• Morag Tong is not only a group of assasins. Their recieve their contracts from Great Houses of Morrowind. A representative of one of the houses / guild point of operation could be in every corner of Cyrodiil, so no teritory restrictions here.
• Morag Tong and Dark Brotherhood do not like each other very much, to put it mildly. MT state to be the only true faction and treat DB as peevish younger brother who betrayed old principles. How many frictions, quarrels, betrays, kills and misunderstandings that situation can create eventually? Here's the tip: many
• Dark Brotherhood work in a simple way - here's a contract and you die - in more or less sophisticated way, for Sithis. Chaos it is. Morag Tong did the same thing in less cult-ish and more ceremonial, honored way. Chaos, yes, but a controlled one. A very, very old tradition that need to be fulfilled. They believe a human/mer life is so valuable and sacred that taken it form someone requires a proper preparation and respect.
• That said, the whole skill line could reflect that approach. No one shot dagger here, but maybe a bow before a strike when using MT ultimate? Killing somone without a contract could send at you some punishment from the faction - it could be adjusted by the guards as usual, but with many kills you could have do a quest to undone the stains on your honor, to allow you to return to your service for the Morag Tong again.
• Unlike DB, fullfil a MG contract in public would not be treated as a crime. Ok, the witness will scream, and be scared, and the guard will stop you, but you will have your contract in your pocket. Showing it to a guard would make him allowing you to go away freely (1-2% to attack you anyway driven by anger). But some contracts will require to be done without any withness and when you kill the target in public anyway, there will be consequences - for example your payment would be reduced by the amount of money as a compansation to the family of the target for a dishonor they experienced by your actions.
• A Morag Tong assassin will be known as, and respect for - at least in Morrowind.
• In PvP as a MG assasin(s) you could get a mission to kill the recent Emperor for a PvP currency

Skill line:
Unfortunately I haven't figure it out yet, but I'm sure it can be done more easily when based on the approach presented above. I wish it would be linked more to the principles of MT, and less to the killing itself or more easy killing like in DB skill line. Maybe you're also inspired by the idea? If so, show here your skill line abilities examples you would see to fit here.