My reaction is that if Kemish said the words attributed to him, it signifies zilch. Ismay admitted to his desire to try the ship out on the Monday or Tuesday. As the trial never took place, so what? Anyway, it's from Pellegrino.
The 23¼ knots has always bothered me. I've only seen it in Eaton and Haas, who, as so often, quote no source. Personally, I think it's highly unlikely, for several reasons.
Titanic had only a skeleton crew of firemen and trimmers, about equal to one of her normal stokehold watches. To hit 23¼ knots they'd need most or all of the boilers and some enthusiastic stoking.
The engines were brand new. Why thrash them?
Nobody at the inquiries mentions the burst of speed. In fact, both Lowe and Lightoller expressed their wish to see what the ship could do. They never hint that she had already exceeded 23 knots.
Unless E & H can produce a credible source, I'd put it down to a tall tale swallowed by some paper.