Sound the Alarm ! - When did Kate Announce Maddie's Disappearance?

The official story is that Gerry checks at around 9.05, comes out and meets Jez Wilkins at say 9.10pm, Tanner sees Tannerman at say 9.12, Oldfield checks at 9.30, Smiths see Smithman at say 9.50, Kate makes checks at 10pm and raises the alarm. I have read in a couple of places that independent witnesses put the alarm being raised at about 9.30-9.40pm. We know that the Tapas 7 cannot be trusted and that most of the Team McCann narrative is there to fool us, so what do people see as the most likely time line for the last hour?  Was the alarm actually sounded twice?  Once by mistake at around 9.40pm and then "officially" at 10pm?

If Gerry is out being seen by the Smiths at 9.50 why didn't she wait until 10.00pm to raise the alarm? Was the original plan to choreograph the abduction for say 9.00 to 9.30 and things went wrong because of Jez Wilkins? Was the plan to send Jane Tanner out at 9.10 to check what was happening? Can anyone suggest an explanation (assuming the timings from the independent witnesses are more reliable than that of the Tapas 7)?