Some insight from your merciless GM as to how you might proceed in...
OPERATION: DARK THRALL
I won't always be so helpful, but given the political nature, intricacies, and the complexity of this mission, not to mention the newness of the group as a whole, I thought it worth providing some direction. Enjoy.
Subversion Endgame
Your squad's ultimate goal for Operation Dark: Thrall-- taking power as quietly as possible!
RP-wise, we'll assume that the group's conversation with Nash, in the Spear's lounge, included the technical aspects of taking control of the Board, in addition to the ins/outs of how power works in the CSA, rather than slogging through a lot of unnecessary gamey technical posts in the narrative.
Take Control of the Bonadan Executive Board
There are Executive Boards on key planets, in key systems, across the Corporate Sector, which control what are called 'sub-sectors' across the entire Corporate Sector. These sub-sectors make up the voting power of the CSA, and are the powers that be that control the laws, resources, and decision making power of the CSA.
In a sense, using real-world terms, you can view the Corporate Sector Authority (CSA) as a country, and the sub-sectors as states/provinces within that country. The sub-sectors are the voting power within the CSA. The Executive Board of each sub-sector is run by a handful of members, who ultimately make the decisions for, and control, that sub-sector, giving them a vote as to how the CSA itself conducts business and behaves as a larger entity.
Most of those Executive Boards, which control sub-sectors, are being threatened by Sith Spec Ops squads just like yours. Your squad, 8th Special Operations, has been entrusted with perhaps the most important piece of the puzzle: Bonadan, the distribution hub of the entire Corporate Sector, which essentially makes it like the 'capital' planet/system of the Corporate Sector.
The Bonadan Executive Board (to clarify, this is what Nash was referencing when he mentioned being placed into a position of power): Anyone who owns/controls 51% of the Board's financial power has actual control of the Board itself, as the voting power of each Board member is actually equivalent to their % ownership. This means that 51% control requires no actual vote, as the 51% is enough to win outright, giving the majority owner dictator-like power, and the control that comes with it.
To Nash's knowledge, from hearsay around the Kraspen underworld, no member of the Bonadan board has 51% control. Furthermore, this degree of control and ownership on any board is somewhat rare, as the Board members themselves are typically good at jockeying for control, working together when necessary to prevent anyone from achieving 51% control. The number of members on any board is variant, but can range anywhere from about 5, to a dozen, depending on how many 'war droids', as Nash called them, are 'patrolling the financial market.' Naturally, each Board as a whole owns the vast majority of their respective 'sub-sector' market, but not that entire financial market, making certain that the 'little guys' never gain any real foothold, as the Board itself controls when, and if, any new members will be inducted into said Board.
The endgame idea for Op Dark Thrall is to be in control of 51% of the Bonadan Board, in any way you choose to do so which would actually give full control of the Bonadan Executive Board, which controls the Bonadan solar system you're in, and the sub-sector attached to the board. All of the Sith squads like yours, across the Corporate Sector, are busy doing the same kind of missions, subverting and usurping seats on Boards across the Corporate Sector. Assuming enough of those Sith missions are successful, the puppet Board members will be able to exert enough control over the Corporate Sector as a whole to control its resources, and decision-making power (e.g., preparing for, and entering, galactic war with the Empire, New Republic, or both).
A note on Board members (again, info provided by Nash during your 'get to know you' session): They are, naturally, very secretive, and stay in the shadows, appreciating that being 'known' would make them huge targets for extortion, assassination, etc. They use pawns, and the like, to carry out their whims, when necessary. Nash suggested that the only real way to get to them was to 'follow the money, and the power'. Sooner or later, it should lead to someone on the Board, as those are the individuals that truly control Bonadan, and the Bonadan sub-sector, which would be a collection of (solar) systems, and their constituent planets.
However you choose to exert this 51% control over the Board is up to you.
Or, you could just say screw it all, abandon the mission, go where you please, and hope the Sith Empire forgets about, or forgives you, and utterly fails in their effort to take over the galaxy.
Your choice.