The likely thing that would happen is Starfleet will conduct a Board of Inquiry using officers from another command or even a JAG investigation. Given the "time travel" aspect of the scenario, the DTI would also be involved.
Have the Committee interview each character and have them describe, in their own words, their reasons for the actions they took and their personal feelings and intentions throughout.
This will give you an insight into the reasons for their actions and determine if they f@@$%* enough that the only choice would be a court martial.
Arise, arise, Riders of Theoden!
Fell deed awake: fire and slaughter!
Spear shall be shaken, shields be splintered,
a sword-day, a red-day, ere the sun rises!
Ride now, ride now! Ride to Gondor!
Theoden King: The Return of the King