Let's assume for a moment that I was wrong (unthinkable, I know) and that this episode has nothing to do with abortions, planned parenthood, or any other contraceptive/fertility/etc message, and instead examine it all anew.
Hitokage directed my attention to the shadows and I confess that the first time through I missed this. In the beginning of the episode Zebra and Fuyubachi sort of look like they have them, so it's possible that the trio was still alive and that their first attempt was a success, considering that they see Komome and then a wrecking ball flies into the room. The next scene has their bodies lying flat on the ground, and they get up and walk away. So it is safe to say that from at least that early in the episode they were dead, and it makes other things, like the man who jumped in front of the train and somehow lived through it, make more sense (if they Zebra is seeing his ghost instead of his actual self.)
The episode's plot is then about the worth of life and not throwing it away via suicide, and demonstrates through the caricature of these three unlucky death-seekers, that suicide is a terrible solution to one's problems. This is made clearest when the three are in the inn, discussing how jealous they are that Fox got to die, and wondering why Lil' Slugger didn't come and kill them, too. The irony is that they claim to have been backed into a corner the way Lil' Slugger's victims were, when in reality the three of them have every reason to live in each other. Indeed, their reasons for wanting to die make clear the reasons they have for living, too: Fuyabuchi is old and ill, and seemingly all alone. Zebra is struggling with homosexuality in a society that does not accept it (and possibly the loss of his love), and Komome is very lonely. The moment she declares "don't leave me behind!" drives the point home: none of them should want to die, because they have each other. They may not be lovers, may not be linked by blood, may not have anything in common at all, but they are, in fact, a family.
At the end of the episode, Fuyabuchi realizes they are dead, but I confess that the first time I watched it the scene came across more as him realizing how much he had to live for in the two people with him. This is possibly because throughout the episode Fuyabuchi's primary concern shifts from "How can we kill ourselves" to "How can we prevent Komome from dying?" until, of course, Komome makes it clear that, life or death, she doesn't wish to be separated from them, at which point Fuyabuchi's motivations become ever more increasingly "how can I keep this little girl happy?" Thus, when Fuyabuchi realizes he has no shadow, that his last pill is still in the case and he has gone for nearly a day without any need of it, and thus the three of them are dead, his attitude changes altogether. He walks hand in hand with Komome and Zebra, and the three of them cheerfully pose for a picture, walking away without regard for the screams of horror of the people they had taken the picture with. The title "Happy Family Planning" then, refers not to some method of birth control, but to the fact that Fuyabuchi, Zebra, and Komome's plan had lead them to become a happy family, as it were.
As noted by others earlier, the reason Lil' Slugger runs away from them, assuming that Lil' Slugger is more than just a man (as the series is presently suggesting), is because the three death-seekers are in fact the exact opposite of the people he has attacked so far. They're not backed into a corner, not isolated, and not altogether stressed out. In fact, for three suicidal dead people, they're pretty much carefree. This sets them up as an ironic counterpart to the people in the series, all of whom are living and wishing desperately for release from their troubles even as they struggle under the strain of isolation, whereas these three dead people are cheerful, enveloped in companionship, and, most notably selfless. The victims always thought of themselves, whereas the dead have spent their entire screentime concerned for each other.
To be perfectly honest, it's wrong to say this episode could have been penned by Kawamori. It's similar in that it serves as a scathing review of the people of Japan and the illness of modern Japanese Culture, but unlike Kawamori, it's actually very subtle, choosing to show what's wrong and allowing the viewer to draw those conclusions and think about them, rather than bludgeoning them over the head with it as Arjuna did. If Kawamori had penned this episode, you would have been told the point and berated for needing it told you, while being shown imagery that likely would have conflicted with, undermined, and ultimately poisoned the message. So, as Shergal said last night, you could say this episode was like something Kawamori had made, but unlike Kawamori's plots, this was actually good.
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