Not being a combat grunt, I think the later would result in less child casualties. No, I don't give a shit about the Cops. They should never have put on a badge and gun if not going to sacrifice all for children at the very least.
There was not one door, but two doors, to rooms 112 and 111, with a door on the interior wall between. So the single killer had to divide his time and attention between them.
Also, I believe there were windows on the back sides of the room. These could have been used to find out which room the single killer was in at any given moment. A simple car mirror taped to a car antenna will serve if nothing better is immediately available.
Police can be on both sides of both doors while out of sight of the shooter unless he opens a door, in which case the police can block the door open and attack immediately.
Police shooters waiting under the windows must be ready to spring up and fire through the windows at the taller male shooter.
If no keys are available, and no SWAT breaching teams, firefighters have tools for prying open doors very fast.
Much could have been done other than waiting for everybody to bleed to death.