The best time for the intruder to get in was obviously right after the departure of the McCanns, 20:30. Once inside through the patio door, trying to smother Madeleine about to scream, he suffocated her accidentally. He remained there, likely horrified and not knowing what to do. The state of the bed indicates there was no fight.
What about Mr McCann ? He didn't say the truth. He checked like Matt did later, he just listened, he said he never looked inside normally. Didn't he admit the predator was with him in the flat ?
What about Jane T ? She saw the carrier not at 9:20, but at 9:45 when she went to relieve Russell. She thought he was Geraldalike and feared the police would go on a false track if by chance someone else had seen him. So she changed the time and gave Mr McCann an alibi.
The man who killed Madeleine left the flat with the little body on his arms and was seen by the Smith family 10 minutes later.
Eddie was right.