Timeline of the 2nd chapter (Matthew's first chapter)

• Constable? Watchman? Gardener? wakes up Doctor in the middle of the night
  "There's been a death I'm afraid Doctor. Would you mind coming to take a look?"
• Doctor goes to Central park and discovers scene for what it is.
  "I'm afraid the night has just begun for the two of us, Mike. Would you please fetch me a telephone?"
• He communicates with the city's highest powers? (whatever they are) and they call in the Investigator
  (I think this totally works out w/ your timeline...I'm doing the back-story of how the Investigator came to Garden.)
• The scene is left as it is, environment is manipulated to freeze everything in time so the Investigator may see it undisturbed
• Intro of Investigator
• Doctor assists the Investigator
• Doctor goes home to sleep, can't sleep and goes to market to wander. 
• The Doctor meets Eve and Gardener, Horten. (for Gardener, see above)
• They discuss murder, current events
• Doctor leaves in mid-afternoon and arrives at home to find communique from Investigator
• They meet and discuss findings of investigation so far and what lies ahead
• Doctor leaves and goes home. He feels old.
• He has a quiet dinner w/ Eve, they have been meeting once a week like this for many years.
• The Doctor dreams of the first planting of the Garden, Chapter 2 will only have half of this dream
• End of Chapter 2
  Chapter 4 will start w/ Doctor dreaming of first planting of Garden

Day 1 timeline laid out a little better:

• Simon Temple wakes the doctor up (I'm glad you woke me up Simon, I was having a nightmare; I don't sleep well anymore."
• They get the Doctor's butler, Hobbes to flag them cab? (they use the doctor's barouche?
  I would probably try to compare the Investigator's entrance to the doctor's....he will be silent and grim, but will know everyone gathered. He will seem the one that will solve everything and calm it all down.
  Am I going to just repeat all of this intro from what you have?
• He examines the bodies
• Compares notes with Investigator (what is his name btw?)
• They decide where to store the bodies until autopsy
• Investigator declares ground-rules for scene and investigation
• They makes plan to reconvene but separate now to settle stuff
• The doctor wanders
• He  checks in at his office (why does he still have one?)
• He wanders more
• Meets up with Horten and Eve. Briefed on different side of things
  (This way the audience has a complete picture as of now of all that has happened up to the investigation of the murder
• He goes home midafternoon as he is tired
• He talks to Hester and Hobbes
• The doctor goes to sleep and dreams of Garden