How did he shut one after he DIED..?
The cops said they had to open it explosively.
He shut it when he crossed over the last time.
Simple.
He then shot himself.
Now the other room is only accessible via the normal hallway door or by breaching the connecting door.
It does present some timing problems.
Overall though, it’s not difficult to lock the connecting door and then go around to get in the other room.
Paddock must have started his shooting in room 134, and then he must have gone down the hallway to get back into 135.
So he must have gone down the hallway after the shooting started.