You seem to be fixated with the idea that the only way to search for a missing person is 'physically.' And yet if you were to ask any of the experts/professional organisations you would learn that that is probably the least productive use of time and money - and that it is keeping the missing person's profile as high as possible for as long as possible in the public's eye which gives that person the best chance of being found.
Traipsing around Portugal with shovels in their hands may make for a good photoshoot - but they might as well be looking for a needle in 10 million haystacks - especially as they don't even know whether Madeleine is in Portugal or not.
Surely the best way to search for a missing person is the one that has already been proven to be the best?
If you wanted to buy a new TV - would you physically travel around to every Store to find out the best deal, or would you pick up the phone or use the internet to achieve the same result in a fraction of the time. It's the same principle IMO.
Okay. You have a witness saying that she saw a suspicious man carrying a child that appears to be your child, a few minutes later you find out that your child was "abducted" (no doubt about it), and instead of trying to go after the presumed abductor you stay in the apartment cleaning your mobile phone from any message in it, calling UK media, calling UK family and acquaintances, calling your friends and their dogs into the "supposed crime scene"..and 40 minutes after you gave the alarm to your friends you call the police. After that you keep inside the apartment walls, because there is no point in following the voluntary search groups that took all night and many other nights looking for your child.
Why search when there were hundreds, or maybe thousands, of strangers looking for her? Better keep fit. Better keep sending the twins into the creche and maintain your tennis lessons and your jogging....And latter give press releases and make photo sessions....
Are you kidding me? Where is it more efficient to keep your holiday activities, implemented by a star syndrome, than looking actively for your child?