I might have to replay through the game again to find that one interlude part, but it's most likely third day. I loaded up the game and I believe the character I interacted with was Hanbee. The game does give me the option to talk to two people, it's just that the other characters didn't give me a choice to talk to them. I believe at that time, everyone was in their rooms? But I couldn't really interact with anyone else except the one person, and then I can't do the second one not because the game won't let me, but there was no one else to do my free time with. I believe this was when you were waiting for the time to meet up with Yuzuki to go to the boys' dorm.
Now as for the event you can access early, it was when you talk to Kanokogi while Hanbee is with you. If you go to the girls dorm at the time that you're supposed to talk to everyone and investigate to know their names, you can actually go into Yoneno's room. I thought this would eat up my free time just from the nature of the scene. From reading the dialogue, it seemed like it skipped me all the way to nighttime, I even went to Yuzuki and for some reason her name is shown instead of "Unknown". Upon playing the game further, I found out that this scene happens the night before the third day, this was a major scene that I shouldn't have had access to very early on.
Wait hold on Jason, "when you wait for Yuzuki to go the boy's wing" ? Is it after crashing the TV and the Camera ? Is Hanbee in his bedroom ?
If so, that is not an interlude phase and this part is actually not meant to be in the demo ...
Besides, I'm currently replaying the game all over again (for the thousand time ;_;) I have fixed the event in which you have access to Yoneno's room, and Yuzuki appearing out of the blue.
If you don't mind, I'll come back to you if I need a few more details :).
Thank you so much again Jason !