In one campaign that I'm running, players expressed a disappointment about the way the game is balanced. They understand that if they want to win, they have to rush to the objective and forget about gunning everyone Rambo style, but they think it makes for a boring game, not the experience they were expecting.
So, since I don't care about losing or winning, I'm thinking about removing the time limit, except in missions where it's really thematic. To try and balance that, I'm thinking about limiting each heroes to one rest per turn. Or should it be a team Rest Pool, say 3 rests per turn.
That is a good houserule. If you remove or delay the time limit, the Rest action becomes too powerful, since the heroes can make it so that they basically never die or get wounded...and that's no fun. Also, pay attention to the fact that not all of the missions have a time limit.
What you might consider doing for to adjust the timed missions is to limit the amount of Rest actions to X per mission. After they've used all of their Rests, they can rest no more. Maybe represent this with some tokens or something. I think you'd have to play around with the number of available Rests, but I think it's better to give them a specific number of Rests per mission, rather than per round.