Have read and heard a great deal about you and your work. Nice to converse with the man himself albeit by the pen!
Forgive me for saying so but you make the same error as have done many other researchers... lumped the three bell warning together with the helm order.
In fact, Titanic was safe and being operated in the (sort of) normal manner right up until Murdoch gave that fateful helm order. From that moment, Titanic had two choices... keep going straight and hit the berg or turn left or right but still hit the berg.
As you know, the 47 second period comes from an attempt by the UK Inquiry and White Star Company people to fit QM Hitchens statement that Titanic turned 2 points from when he received the helm order until the time the ship hit the ice. They simply turned Olympic 2 points when travelling at 21.5 knots and found it took 47 seconds to do so. However they were not comparing like-for-like. Olympic did not have a sudden sideways effort imposed on her bow during that trial!
Subsequent researchers have matched Olliver's 'walk' to re-enforce the veracity of the 47 second turn theory.
The first half of the 47 second proposal ... the alleged 41 seconds before the helm order was given is the part where Olliver can do his walk from midship (the standard compass platform)to the bridge. I have measured that distance the base of the Standard Compass Platform to the bridge and walked it myself and I agree, it would take, as you say, 45-50 seconds (allowing for ladders etc) for a man to cover that distance.
If Ollivers did indeed hear the three bells and immediately left for the bridge and saw the berg as it had just passed the bridge then the moment he saw the berg was about 7 seconds after impact and 13 seconds after the helm order was given. If this were so, then the bells were sounded 34 seconds before the helm order was given. However, the Lookouts stated that the ship's head was turning at the time when one of them was still at the telephone. This places him at the telephone less than 6 seconds before impact. All of this points to the lookouts having waited almost 30 seconds before they rang the bridge and to Murdoch having seen the iceberg at or just before the moment the Lookouts decided to use the telephone.
This 34 second period re-inforces Hitchens's statement to the UK Inquiry that he was given the helm order 'about half a minute' after he heard the three bells. However that statement contradicts the statement he made in the US when he said the helm order came almost immediately after the three bells.
Is it possible Fleet had a word with him in the lifeboat or on Carpathia?
That first half of the 47 second period is academic but there is absolutely no doubt in my mind that Murdoch gave the initial helm order 6 seconds before the ship hit the iceberg and there was no way under normal circumstances that Titanic changed her heading 2 points in that time.. However, I do believe she did as Hitchens said she did but it was not under normal circumstances and the ships head was turned more than normal because of the assistance given by that lump of ice.