Control:
So, how d'you wanna do this?
This can be done as an actual scene, a metagame discussion with dice-rolls, or a quick-n-dirty set of dice-rolls and a narrative wave to make it go away.
Either way, I want to know what you want and how you want to approach these guys. What do you want from the scene or prose discussion? So... what does success look like?
Oh, rolls and resolution is probably a solid choice.
So, Baylee's strategy going in will differ based on the interview. For the mariens, she wants to assess their combat ability but has also been made aware of the internal connections and mistrusts those. She wants a cadre of fighters loyal to her who will have her back. So, she wants toa ssess those who would break loyalty with the sergeant and switch to her. Honestly, on the face, she's quite likely to reject Karin and the Sergeant out of distrust more than anything. But, this is why having CSX along would help to that.
For the non-combat passengers, assessing their motives and goals would be her aim.
Now, Baylee is a very direct and straight-forward personality, but she's not easy to fool. She'll straight ask the marines if they'd could see themselves being loyal to her. She'd sincerely offer them berths, positions, and equal shares to the rest as well as her support as captain. If they honestly and sincerely accept, fine. If they lie and try to join, rejected. If they hesitate or want to leave, she might try to convince them.
All marines will be offered a light sparring session, even crippled one if they feel up to it. Anyone other than Marines who might want a combat position are welcome to spar as well. Sparring will happen in a group though. She wants them all to see her best the sergeant, because she absolutely believes that she will.
So that combat might be fine to play out but the rest could be rolls or quick vignettes. I don't want to slow the game but this is important for Baylee's arc I think. Other crew are welcome to sit in as well. Baylee's always happy to spar with anyone.