Just running in and completely ignoring stealth is the best approach to this "stealth game" due to the disgusting lack of areas the AI can go, basically making most of the residences 50% harmless with the amount of save havens you can easily run to. The Bakery's roof, The Mayor's hanging raft things, basically anywhere in The Museum. Not to mention the fact that it can give up chasing as soon as you go into a different room.
This is due to the AI not being able to jump or leave the building that they're in at all, and combined with the fact that they will completely forget about your existence when turning a few corners or going into a room.
First of all, the AI should definitely be able to walk out of their attack zones, The Baker should be able to go onto the roof and chase you out of the entire establishment, The Mayor should chase you into the backyard, and Mr. Peterson should come outside onto the Museum grounds, balcony, or rooftops when provoked or if he sees Quentin to catch him.
Secondly, if you turn a few corners and the AI can still hear your footsteps running, they should be able to realise that you are still there, so that they would continue running to where your footsteps are coming from, but will not know your exact location. This would also allow the AI to cut you off and surprise you more.