I think this would be a very effective approach, and not just to the Titanic, but to other FFs.
But I think you made a sharp turn between the paragraph ending with "sunk a year before" and the next paragraph where you pretty much concluded that a murder took place. I'd move the conclusion closer towards the end, and use the in between space to build suspicion. So I'd move the buildup paragraphs about flares, radio, unsinkable illusion, insufficient life rafts, and risk for scheduling, so that they are preceding the detective's conclusion that it was murder.
Also, I'd play with the detective's deliberation in the process. For example: Could someone really sink a ship full of people just to murder a few? Who'd be capable of something like that? What would they gain from that? So that the reader follows the natural progression of the detective's thought process.