Eddie searches for the location of the strongest scent. As soon as Eddie entered he picked it up according to Grime so he then searches for the source. First alert in the parents bedroom and the second behind the sofa. That bedroom door could've been unlocked when Matt checked but it doesn't mean it was still unlocked an hour later before the police arrived.
Outside of [the other] patio door: One inadequate print was recovered.
SY brought everything back to zero which means everyone is a suspect.
Your theory has become so complex & convoluted I'm not sure you even believe it now.
The bedroom shutters can only be closed from the inside. Do you really think that Gerry put the corpse on the verandah, nipped back in through the lounge patio door and locked the bedroom patio door, neatly arranged the long curtains, nipped back out the patio door, put the corpse in the flowerbed, nipped out the garden gate to check the coast was clear, nipped back & popped the body by the wall adjoining the alley, nipped back out the gate again, hot-footed it round the corner, retrieved the corpse and made his way to Block 4 car park & beyond?
Or did Kate close the shutters, lock the door & re-arrange the curtains after opening the shutters & window in the children's room to simulate a break-in when she went to the apartment at 10pm?
All, of course, completed without leaving a trace of cadaver contaminant anywhere.