I found it's best to dismiss most of your generic soldiers once you finish most of the Propositions to leave space for monster breeding. Breeding one monster class at a time is the best way to go. Once you've finished that, you can fill up your remaining slots with generic soldiers and monsters. This way I've manged to keep all my nongeneric characters. I dismissed Boco though.

You can still recruit characters with a full roster. But the game will prompt you to dismiss someone to make room.