Steam recip engines can go from full ahead to full astern instantly, that is why the old steam tug masters had such a job getting used to diesel engines which have to reduce revs for the gearbox to reverse the shaft for them. I have worked on a steam recip ship with a single rudder, when the vessel was dead in the water you ignore the rudder, it is the paddle wheel effect of the screws which turn you, ie right hand throw and a left hand throw props when going astern and ahead. I would think that these destroyers if they have opposing throw propellors would be quite manoeuvrable when stopped in the water and being steam recip the power would be as quick as the telegraph could be read and applied in the engine room which would be quicker than many people realise, especially on a naval vessel with a large engine room crew.
Also looking at the close up of the bows, it looks like a bobstay on some hanging off the bow, with a ring which could be quickly slipped over the end of the spar and the stay adjusted for tension.