I think it would have taken Amy ten minutes to get to 5A, search it, and alert Lindsay. It took Lindsay five minutes to get to the Tapas. We then have to allow five minutes for Emma to go and get the description of Madeleine clothing. That means it took twenty minutes to be at a point to begin searches. Assuming that the five 'team leaders' for each search zone had arrived, gathered their teams, and were poised to begin, we can allow another five minutes for them all to move off to their designated zones.
John Hill says he was phoned by Lindsay at 22.28. He arrived at 22.35 by which time 100 people were searching and calling the child's name.
That means that Amy must have left the night creche for 5A at 22.10; twenty five minutes before John saw all those people searching.
In my opinion she phoned Lindsay after the woman arrived at 22.05, and Lindsay told her to check it out. No missing child procedure is triggered by a rumour, it had to be confirmed. Amy rang back and confirmed the disappearance following or during her visit to 5A. That was between 22.15 and 22.22 in my opinion. Lindsay then rang Emma.
After searching 5A Amy went to the Tapas complex and probably helped with organising the paperwork for the search teams. At 22.35 John Hill arrived there. I think he and Gerry went to the main reception together to phone the police, although both had mobile phones and the Tapas was nearer. Perhaps it was thought it was more appropriate to use an 'official' phone.
22.41 was the time of the first call to the GNR. From Amy's point of view that was 20 minutes after she officially raised the alarm by notifying Lindsay.
You said "I think it would have taken Amy ten minutes to get to 5A, search it, and alert Lindsay"
I think that is pretty good, and considering the call to Lyndsay would have to precede the call to Emma (10:17)
One could imagine on that basis the call to Lyndsay could have been 10:15 (i.e. 2 minutes before calling Emma).
10:15 minus 10 minutes and you get 10:05 the time the lady mentions the man.
So as long as Amy hurries around to the McCann's apartment and leave the creche immediately it would be possible to present her self at the McCann's apartment around 10:10 and the spend the next 5 minutes checking the apartment and going off to ring Lyndsay by 10:15.
You wrote: "After searching 5A Amy went to the Tapas complex and probably helped with organising the paperwork for the search teams. At 22.35 John Hill arrived there. I think he and Gerry went to the main reception together to phone the police, although both had mobile phones and the Tapas was nearer. Perhaps it was thought it was more appropriate to use an 'official' phone."
Now that is speculative but entirely possible.
"22.41 was the time of the first call to the GNR. From Amy's point of view that was 20 minutes after she officially raised the alarm by notifying Lindsay."
I might have calculated that as 26 minutes rather than 20.