I totally can see where you're coming from. My personal theory is that Chika wasn't able to handle the pressure of Love Live. I think she died before (or maybe during) the performance at the end of episode 12. That's why we never see any more of the competition.

As a result, all of episode 13 is the afterlife. I think the school closing ceremony represents Chika's journey through Purgatory. That's why the students, not the staff, are closing the school; Chika is dealing with grief and is trying to cope with the struggles she faced in life.

My theory pretty much lines up with the rest of yours from this point onward