Putting her in J=J is the most sensible option by far.
Going solo makes no sense (not a single ex H!P / 48G / Stardust idol has managed a lasting and successful solo career).
TF, MM and Angerme don't really need her.
No one remembers how many O's is the hot new thing, so not worth the risk of associating it with KF.
A new group? It would be stupid to take the focus away from how many O's so soon.