I’m in a similar position, so I went to their other ‘game’, ‘what’s your story’, which has the…I guess Alpha release of LoveLink, and on there, I discovered that basically all the people I hadn’t hatched with yet were copied stories, I suppose so that people who are interested in a different type of facial structure or something still get to experience the same story. I have a theory that the other people who aren’t copies aren’t finished yet, at least up to a point where they can put them ‘on break’ before writing more.
As for the other thing you mentioned, putting people on break to create an active slot, the support team have stated multiple times that there is no limit to the matches you can have. I think if you wanted to, you might be able to find a way to restart the game, but if you’re not interested in that, the only thing you can do is wait.
I really hope that they’re going to put out something new soon, but time will only tell. I’ll be happy to wait as long as it takes, if the end result is excellent.