I don't think Akira will be the one who spreads it around. When Chika moves in, she's obviously going to tell Yumi and take along. Even if she doesn't go, she'll probably tell Yuki about the cheap, nice place her friend moved into. (during an argument probably), and then when Yuki goes to the dive bar she'll bring it up when shes around Rika with Imani ether in the bathroom or just not there that day because of problems that a new apartment could fix. Why would Tsubasa allow all these people to move in you mite ask well the whole plane is to make Chica feel like she found the place on her own. I believe that to keep the white lie going Tsubasa will end up letting more people move in and that will ultimately lead to her loss of control over the situation (Hopefully in a comedic manner and not a tragic one)
Basically, a game of telephone is going to happen, with Imani being the last to hear about it and actually having to move in with Akira in the end. (The last bit might be me smoking a bit of copium.)
This is probably the most possible and welcome way for everyone struggling with lives to access this solution.
However, other than Yumi, Tsubasa might not deem Yuki, Rika, or Inami as necessities for Chika especially this is now about ALL her daughters living in the same building; she would do all she can to boycott who gets to live here: people need to be qualified in her eyes, not just in need. She is a puppetmaster with her plannings devoted to an exclusive group of people she cares about, not a charitarian after all. And we definitely see how little Sensei has a saying in this and how incapable he is to exert himself for others with obvious financial needs.
I don't think it's easy to convince the Yamaguchis to move though. Yuki is well content with what she's still managed to gather, and Yumi might take this chance to just try to be more independent from Chika (which ultimately nails the coffin and leads to Chika deciding not moving because of her); plus, the both of them share the same "we the shitty people ain't fit for this" mindset.
Inami, on the other hand, might be able to usurp and become Tsukasa's tutor since she's good with kids and also a strange type of teacher, then uses as a leverage (of course passing Tsubasa on this one is nearly impossible)
Speaking of Tsubasa, how little she minds about Touka's intention really surprises me (I found myself not being able to read all Tsukiokas well TBH). Three events, one about Chika, one about Tsukasa, and one about herself; not one is focused on Touka.
I get that she does have full confidence in her more mature daughter and treat everything as some type of learning. But that "You could lay as many fingers as you want on her and I'd think nothing of it" is quite the jaw drop for me (not to mention the
arrangement she spoke of when
both Chika and Touka can no longer sate him). I guess in other NSFWs it would a
HELLYEAH advancement, but here I found saying
wait what more often than not.