I could see having the mechanic be that the body can be hidden until the end of the school day, which means that the moment club time ends, any not-properly-disposed-of body would be found because of smells or the teachers checking the usual hiding places to make students go home. Any not-hidden bodies would be found during class time, because teachers not currently in class would move through the school to check for students playing hooky in the empty classrooms.
Disposal could consist of smuggling bodies off school grounds (while the school is empty, so that
technically wouldn't have to be shown), the incinerator, and putting the body beneath-or-in trash bags in the dumpster. Hiding the body would be a temporary fix, so that you could attend class or not miss important events in the game, and could use suggestions like what
@LucasSomething brought up. Things like hiding the body in the music case (I never really cared for the kidnapping method), hiding it or its pieces in the compost heap in the garden area, and other such places.
Then during club time, when there are way less students around, you have a better shot of disposing of the body without somebody seeing you. This would also limit how many people you could manage to kill in a day, because of limited access to hiding places (you can only use the compost heap if you're in the gardening club, for example), and because each disposal method can only get rid of one body at a time. Any bodies left in the school that aren't in the process of being disposed of are ALWAYS going to be found, and the more bodies found, the more likely the player is to get caught.
Also, auto fail if you slaughter everyone in the school, because that's just fucking obvious.
Edit: I wrote this while tired, sorry. So many typos.