Well, I was fortunate enough to get this done last night. I followed some of the suggestions here in the process. After resetting the mission, I joined forces with the only other player on my server running The Oppressor at that time. I joined his mission in progress. He had already taken care of Reactor Alpha. He started to go for Gamma, but I suggested Beat first. We did those in order, killed all the mobs on the ship, completed the battles and escaped. Then we ran my mission. Same process. All reactors in alphabetical order, killed all mobs, finished battles, escaped ship.
When I returned to my own ship, I was able to use the holo-terminal to speak with the Council before heading to Tython. Once there, I was able to successfully talk to the Council and complete my mission. However, the other player I ran through this with ran into the same issue I had just a day earlier (unable to use the holo-terminal on his ship, 'Council not in session').
He reset his mission and I helped him get through this again. Same process, except I was with him from the beginning this time. In the end, he was also able to successfully complete the mission.
While the sample size is small, the common thread here was that my first time through on Sunday night was also joined by another player while the mission was already in progress.
Maybe that was the problem for most of us and maybe not. Nonetheless, I would recommend anyone enlisting the help of others on class missions like this reset the mission once the group is formed.
Good luck and thanks to everyone in this and related threads for providing info to help me get through this mission. May the Force be with you.
