I agree the cadaver dog & CSI dog are not person-specific. To give reasonable consideration to your theory, it must be assumed that the both the item given to the S&R dogs on 4/5 contained only Madeleine's scent & the route the dogs followed was travelled by her after 9.10pm on May 3rd.
If the front door had not been double-locked (a major question mark there imo) then Madeleine could have exited that way, albeit straight into darkness & towards the source of the disturbance which woke her. From the image below, how many times are we aware of Madeleine using the route outlined? Once? Surely the more familiar route was across the car park & turn right onto Rua Dr. Agostinho da Silva?
You said you favoured an accident in this theory. Where on the route would that have happened, iyo?
All comments my opinion only.
I would expect that the parents would have provided a good source for the scent on the basis they would wish the exercise to produce a result, but there is an assumption that the scent source was provided in good faith.
The dogs could not discriminate date/time any scent was laid down. The requirement for bare feet, combined with the known fact that the shoes remained in the apartment, is a pointer that scent could have been laid down at the relevant time. It is not definitive, and it can never be definitive. IMO there is a tendency for parents to put shoes on their children when they leave at normal times. Therefore, there is a pointer, or more accurately a very real possibility that the dogs tracked MBM.
There were three potential exit routes from 5A:
1) Front Door
There is no reported evidence this door was deadlocked. This exit route ties up closest with the scent trail. If the door was confirmed to be deadlocked, and no other exits were available this theory would be disproved, but there are other exits available.
2) Patio Door
The door is accepted by all parties to have been unlocked. IMO MBM could physically open this door. The stair gate would provide an obstruction, but it is possible to climb over the gate. I think the stair gate provides more of an obstruction on any return journey, because of the location at the top of the stairs. If MBM exited via this route she may have found it harder to return.
3) The Window
MBM could open the curtains and window. But, I believe it is unlikely she could raise the shutters. A test of this would have been useful. There was a case in Egypt at another MW resort where a young child 'escaped' from an apartment, which was subjected to 'listening checks'. Presumably this apartment would have had shutters, which were opened by the young child. But, on balance, I believe this exit route to be improbable.
On balance I favour the front door for exit, but the patio door is a viable alternative.
I will provide some views on route and possible accident, or indeed possible abduction, later today.
All IMO. Also, this is not an attempt to discount other theories, such as abduction directly from the apartment.