Remember roleplay isn't allowed on the forums, and some of the ideas about "story" and so on are getting rather close to it.
I say don't impose anything on positive and negative beyond the actions themselves. Let the players decide how, if at all, they wish to interpret their teams.
Amending the core gameplay isn't out of the question. I think the "swap" move SkyFall mentioned above ends up being too powerful though.
The established 5 minute rule should stay, as should the de-facto practice of omitting the action - with the 5-min rule and people's usual teams becoming well known, that's never been a problem.