I had a thought on this yesterday which, to me, kind of ties up all the loose ends as a theory. Obviously I may be completely wrong or this could have already been discredited, but hear me out.
Basically, the last check on the kids prior to Kate finding them was done by another member of the Tapas group. From the documentary, they mentioned that Gerry was going to check until this other person volunteered (can't remember his name).
So what if he is involved in something shady and he goes back to the apartment and gives Maddie to the eventual kidnapper? It sounds too simple and may have already been looked at, but it's just a theory. Here's why it adds up:
1) I believe this person changed their story about what they witnessed when they went back to the room to check. Perhaps they were genuine, but they claimed not to have even bothered going into the room, then also claimed they noticed more light entering the room and the door was ajar (this serves to lead the police on a different path). Yet they still didn't bother entering the room.
2) Again, may have been harmless, but they insisted they go check when Gerry, I believe, was going to go and check.
3) This explains why nobody else in the group is aware of this and their stories corroborate - because it was only the one person involved and they believe that this person was simply checking the room, as they had all been doing already.
4) Often in these cases, the last person to have seen them alive or somebody close to the victim is involved. This ticks both boxes in a way, despite him claiming to have not checked on the kids, though we've all been looking at the parents for these very same reasons.
5) If you don't believe that the parents were involved then we know that she was kidnapped. The question is why was she kidnapped? People don't like to hear about trafficking etc, but there is a reason. If you accept that these are possibilities, then perhaps this person is involved in these types of organisations in some way. I've seen a lot of things written about the McCann's and their friends which don't paint them in a good light, but perhaps this individual actually is involved with something.
6) If she was kidnapped, it had to be somebody that knew that Maddie would be unsupervised. Perhaps it wasn't a case of a kidnapper watching them for days, but somebody on the inside that knew they would be undisturbed if they were the person to go check the kids.
7) Theories suggest the Tapas group were friends with Clement Freud. Perhaps he was involved in this, or the Podesta brothers. Though that may be a stretch.
tl,dr The person that voluntarily checked the kids (but apparently didn't enter the room despite noticing odd things), before Kate discovered her missing, may have been the person to hand over Maddie to somebody else. No break in, no fingerprints, no DNA. If this was the case, Maddie would have been gone at least 20 minutes before Kate check and a long time prior to police arriving. Therefore, they could have made some distance by the time the alarm was raised.