Reviewed this yesterday before last post but something went amiss. Grrr. Anyway, a lot of what I had to say was to concur with what others had commented already - the inclusion of the council is great conceit adding huge plot potentials, character interactions and conflict. The possibilities for political intrigue and jostling for power and influence is just too rich a vein not to be explored. I hope we see some of the like developing over the course of the story. But then I like dubious alliances and backstabbing in stories.
As others have said, this is bound to be a major headache for Adele. A huge source of frustration and a bureaucracy to contend with on her own ship never mind Admiralty. The fact she has an Admiral onboard as well as these advisors only compounds her issues. The Admiral in question too seems too wily and clever by far. In a way he has managed to subtly undermine and chastise the captain in front of the council but without making a negative impression of himself. I don't think I can trust him too easily and can see why Adele might be more than wary of him. He has huge potential to cause chain of command issues and power struggles later on.
I liked the concept of the council for it only makes sense considering the scope of the mission and the size of the ship. It explains too why a relatively inexperienced captain still finding her feet and command style could be given such an important job - with the council there to defer and/or ratify treaties or global issues. Especially so in light of Janeway's tenure in the Delata Q as the de facto Federation presence. No doubt upon her return many with Starfleet took umbrage to many of the decisions she took. This is their way to curtail damaging decisions made on the say so of one person.
I also liked how the captain is still finding her feet and is not quite comfortable or dominating this council. That'll be something she has to work on - unless the Admiral undermines her further. But it shows a character with potential to grow and change. Looking forward to seeing more of her development.
And again the idea of the council is a novel approach and shows the thought and attention you've put into this story. With the scope of the mission and the size of the ship little surprises and touches such as this are to be expected but all too often can only be hoped for. Really and truly a well turned out job.