At the start of each mission, I do not turn on my expanded outposts right away. Instead, I run around in vehicles on my unhappy characters, squishing the hordes that spawn. As soon as the character I'm using is in a happy state (smiley face regardless of what the word is), I then go back home to switch to another sad face character.
Doing this will often turn 2-3 of my characters happy from the very beginning of my play through. Once the "too many hordes" goes away on the map screen, I then turn on my outpost traps and go back to work as usual.
I'm currently playing with 23 characters and 3 bed facilities (24 bed) so that the only way my people get sad is if they have domestic disputes or recover from illness/injury. Sometimes I log in and nobody is upset at all! Because so many people are happy gathering resources (see infinite resources strategy) and sleep deprivation is a non-issue (see sleep deprivation strategy) I literally could last forever on this level. Last time I logged in I made 1 materials even though I should have lost 19. That's because of all the assertive people in my group making supply runs during the simulation.
I am torn between moving on to the next breakdown level and just seeing how long I could last with this group of 23. If I wanted I could destroy my kitchen (only non bed facility besides built in stuff and medical facility) and put in a fourth bedroom. We'll see ;)
As always I am headache4you on XBOX if you have any questions.