Solomon knows everything that you. the player, knows. My information may be accurate or may be faulty, so I am willing to be corrected.
AFAIK, all it takes is the agreement of twelve magi from four covenants. I suppose it needs ratification from the Grand Tribunal. I think. That may be a fifth edition deal. But I imagine provisional tribunal status would be easy to come by if all other qualifications are met and a Quaesitor ratifies it.
In Provencal and Iberia, both of which operate according to standard customs (unlike every other tribunal of the Order with strange unique rules), I think all that is needed to exit Tribunal is to stop showing up. Which is why Provencal has been unable to annex us.
The situation at Val-Negra is (mostly) as is written in Faith & Flame. What I wrote there is based on a story I once ran here. References are available here. None of those players are with us anymore, so we can feel free to change things to suit our needs and to line up with (what is now) Cannon Val-Negra.
But simple facts remain the same. During the Schism War, it was infiltrated by Diedne archmagi who burned the library and opened the Iron Door and broke the seal. They were all killed, and it took the combined might of two archmagi to reimprison the thing within and close it up. One magus remains, Abaddon of Tytalus, who stands eternal vigil guarding the place. To learn of current state of affairs and inquire about possible revival would require an expedition there.
Aedas Mercurri is Doisettep with another name. They were formed by other survivors of Val-Negra and consider themselves the true heirs to Flambeau's legacy. They believe the truth has been altered (this is also now Cannon).
Duresca would not likely participate or support this idea. They can be convinced, but they will probably not want to part from Iberia. They are also on the opposite side of Iberia from Barcelona. Barcelona is close by and will be easier to convince.