Actually, I think I've got a decent guess at it here. The headmaster killed her during the meeting, and animated the corpse to walk itself to the classroom. On the way, it bumped into Miriam, and that's why she's in a tizzy about how weird their meeting in the hallway, because she probably just, like, brainlessly groaned at her. Because it's being animated, perhaps all decay had stopped and that's why the estimated time of death is over an hour later.
He stole Miriam's sword long ago for the murder in an attempt to frame her because of her family's influence to get him ousted, and planted fake evidence of her cheating to establish a motive. When he went to stash the weapon in her locker, he got the construct to do it. However, the nameplates were switched, so it got planted in with Wallace's stuff instead, since that's where Miriam's nameplate was at the time. Then he gave it a few more orders, but one of them wasn't possible, so that's why it's stuck inactive in the locker room.
Meanwhile, he illusory disguises himself as her to make an appearance to further establish the time of death was later. I still don't know what bumped into Jan because none of the spells I have info on can fully explain what it is. An animated corpse can't speak the "be quiet" it said, and the two illusory spells don't have a physical form. So I'm stuck on that one part, but I'm pretty sure I've nailed most of the rest of it.