Alright, finally sat down and recreated the bug for you. Exactly what I did was:
1- Monoghost password is turned on, before interacting with the girl in onyx ward at all.
2- I save the daycare couple, also without interacting with the girl.
3- I finally speak to the girl. She isn't set to acknowledge that you've already saved the daycare couple in her first dialogue, so she just asks you to check things out.
4- In my original playthrough, I realize 'wait, gotta turn on the sunkern switcher if I want the basculin egg.' I save the game before her second dialogue, where she gives you the egg.
If I speak to her again now, without doing anything else, I get the frillish egg, and everything is normal. If I leave, turn on the sunkern switcher, and come back, then I get an error message and the arrokuda egg instead.
Edit: bit of testing. Turning off the monoghost password changes nothing at this point. That is, I still get the frillish egg if I don't hit the sunkern switcher, and an arrokuda egg (with the error message) if I do.