Gorilla Construction Adhesive. Dries in 30 seconds. Just before you are about to do your thing, apply all along the edges of the door, then close the door. It will be hard to open.
For an added measure, since the door opens inward on the stairwell, it needs a handle on the stairwell side. If you remove the handle, it would be harder to open the stair door without tools.
At this point I’m not even sure what they mean by “blocked”.
Blocked to keep it from opening or blocked to keep it from closing?
How would any of this help the shooter to escape? It seems incredible to me that he would think he could do it. Maybe if he had someone else in the motel helping him?