Why not let the characters choose a starting skill, and then just hope they fit into suitable roles to fill a team? Then somehow select one (volunteering, randomisation) to be the officer, and if the mission fails then the officer is dropped for the next mission or something. If it succeeds, then the officer gets to fire on of the others. Ha. Actually that's kind of a spoiler for my own rtd, I was just typing to myself really.
Or even an officer is selected for each mission and then gets to choose a team based on the limited intelligence he has. So to speak.
Actually yeah, I was thinking of a punishment/reward system to work its way in too, a teeny bit like your RTD. 
So, I could let the characters pick their own skills then just stick with that as a team, but assign an officer each time. If he does well, perhaps they get some more equipment, or money/tokens, or indeed to fire one of the others. This could work. Make it kinda competitive. Hmm. OOH. Or, I could let him pick the team, and the others would stay on board the ship... Okay, I might drop this entirely in favour of a more competitive game, cuz there's more room for fun there.
EDIT: Now all I can think of is something very much like yours, whereby I put them in to random teams who are directly competing against one another, before I start kicking people off. Would it be okay with you if I tried something like that?Alright, plan has been rethought and Plan B put in to action.
This would be a different style completely (hopefully comedic, as it's more fun for both parties), whereby I will start with 12 players. These'll be split in to different sized teams for every round, sometimes even individually. The basis of the RTD would be the Ever-Sim, a machine which can take you to any point, any situation, ever. Oh yes, I just want the freedom to do whatever I want with my hapless players.

I'd use a point based system to both encourage team-play and individual, working something like this:
For accomplishing the objective: 5 (only the first team to complete it would receive these points)
For being alive (in-sim) at the end: 1
For accomplishing side-missions sent by moi, via PM: Varies, depending on difficulty.
This (I hope) would make winning as a team useful to the individual, but not everything, hopefully getting some interesting lone wolf behavior at times.
Rolling normal d6, people could be knocked out of the sim for failing certain rolls, being killed or failing to meet a requirement for the mission (no civvie kills etc) and would take no further part in that mission. Further down the line (sounding a lot like la's now

) people would be knocked out until I'm left with fewer, maybe 6 or 4 to pursue something which my thinking hasn't got to yet.
How'zat sound for y'all?