Tiller extension or joystick?
In "parts of a sailing ship" you explain the function of the tiller extension. In Dutch this stick is called 'kolderstok', which in English literally means joystick. When in the heat of the race, I would prefer the use of the shorter word.
In the ships the Dutch used to conquer large parts of the world during the 16th and 17th century, the poop-deck (from where the ship was commanded and steered) was built several decks above the rudder and tiller. To bridge that vertical distance they used a long beam, hinged somewhere in the middle, connected to the tiller with a collar ("kolder" in contemporary Dutch, later used in other contexts in the meaning "funny nonsense") and above deck with tackles to the steering wheel.
As a lot of Dutch nautical words and expressions were adopted by Western-European seagoing nations (even with a Russian sailor it is nowadays relatively easy to discuss nautical matters) the word kolderstok came to English in the form of "joystick".
So, proud of my Dutch nautical ancestry and also admiration for yours, I would like to suggest you use "joystick".
In English and in my entire time as a sailor, I must confess, I have never known it to be called a joystick. I think that the translation to English from Old Dutch may have changed over time from what you now call a joystick to what we call a tiller (and the tiller extension is simply an extension of the tiller).
Also more modern dinghies that go at a faster speed are more likely to heel alot more and go in stronger winds. This means that you need to sit further up the boat and further out the boat requiring the use of an elongated tiller (or tiller extension).
However it is interesting that, that word came to mean a joystick in English since it was in fact a sort of joystick in the manner you described on the poop-deck. The nautical language changes must have happenned relatively recently with the appearence of more high performance boats and skiff that required a longer tiller.
However the change from joystick to tiller, I am unsure of and it may have just become a more popular name.
A very interesting question and one I cannot answer with full confidence and so I hope that other members of the community might be able to help you further. A great bit of the history of sailing there and most of it I didn't know already!