I don't think spacefaring civs will have NO way to solve over population. Allow me to make a few suggestions.
Sex ed. Actual useful education without the weird religious hangups a lot of places have. Mandate contraception, and require people to have a stable marriage partner before breeding. Remove tax incentives for breeding.
Extreme methods. Ban on natural birth, forced sterilization, and state controlled reproduction.
Anime draft. Conscript all females of breeding age into the military for no reason whatsoever. Make up some reason why women are desirable or even preferable to men. It could be some laughably impractical weapon system that only women can use. Not just any women though. Only high school age girls are able to use the weapon. Well there's this one dude that can but no one cares about him.
Sex ed. Actual useful education without the weird religious hangups a lot of places have. Mandate contraception, and require people to have a stable marriage partner before breeding. Remove tax incentives for breeding.
Extreme methods. Ban on natural birth, forced sterilization, and state controlled reproduction.
Anime draft. Conscript all females of breeding age into the military for no reason whatsoever. Make up some reason why women are desirable or even preferable to men. It could be some laughably impractical weapon system that only women can use. Not just any women though. Only high school age girls are able to use the weapon. Well there's this one dude that can but no one cares about him.