Alright for those of you struggling, I found an exploit to escape the school with Daisy. After you leave the gym go upstairs, go right to the next hallway, use the second stairway down. The teacher if your game isn't broken should be staring at the door with her back to you. Hit the W key and it will tell you that you can't, so go into your inventory and open your phone in the essential menu. Click on the blue B, click on the school logo at the top left, click on the green ? at the bottom left, exit your phone.
CLick the W key and magically this time it works. Choose Bug Fixer, choose character stuck, choose unlock character. Now be very careful and walk south into the black area and move towards the front door keeping as much space between the teacher and yourself as possible. You can walk through the door towards the teacher, only leave one space between yourself and the door and now lock your character and you can walk out of the door and continue on with the game.
If there is a way to do this without exploits I must be too dumb to figure it out as the teachers can spot your through walls instantly and if you spend too much time searching they will start to patrol and run at light speed right at you. If anyone has an in with Beggar, tell him he really needs to either play that mission again and see how broken it is or make it a lot easier to complete.
Hope my little walkthrough helps someone.