I just managed to finish the quest:
- I did not choose "Barry's depressed" when talking to the cops at any time.
- I chose dialogue option for Body after knocking on Barry's door.
- Inside the apartment, at the end of the conversation I chose "People die. You move on.".
- After talking to Barry I didn't talk to the cops yet. I went straight to Andrew's grave, which can be found nearby the tarot card Temperance.
- Finally I talked to the cops and told them that I've visited Andrew's grave = quest finished.