Maybe he was pushed down the stairs, then dragged to the elevator entrance, stabbed, then pushed once again?

I do have to agree with the blood though... unless the culprit managed to stab him quickly before dropping him into the shaft. There was even blood in his room and that weird picture he drew, but not anywhere else.

We could always manage to try and find any traces of blood that might have seeped over onto the walls of the shaft.