So I've came to realization there's in fact no issue with Mumei's schedule, Fauna's or anything like that.
The JK tournament was meant to be 3 days long.
https://twitter.com/moricalliope/status/1494904831307173889Fauna is just getting an anticipated start because she had stuff to do (likely for her future ASMRs) and Mori gave her the green light for that. So I'll guess that Fauna and Mumei will stick to the main game and maybe they'll stick together in Vchat or something. I don't know about Bae since there's no schedule but she could be likely to join the tourney seeing she went pretty far.
That said, I can expect Mumei to jump in Ina's chat during her karaoke and Fauna's JK before doing what she's planning - guess we'll eventually get very early lifesigns today. There's also Mori's stream but I don't know what to think about it if it's just a short stream or she will go ham to putting times.