Great question, and Half Moon may or may not have had that. I did some digging and found several comments that the high stern castle had to do with being useful as a retreat of last resort if the vessel were boarded. While that does not answer the question with absolute certainty, the following may still be interesting to some folks regarding the overall design used for the replica. Researchers consulted the archives of the Verenigde Oostindische Compagnie (Dutch East India Company) and Robert Juet's logbook for details of the type and size of the ship for the half moon. They settled on a set of plans of a ship that was thought to be a sister ship. The replica was built in Amsterdam and then transported to New York aboard a Holland-American Line steamship, 'Soestdyk.' The plan below regarding the 1909 replica is held at MIT. There were some very influential folks involved for the 300 year anniversary such as J.P. Morgan, Andrew Carnegie, and others. Allan
The 1909 Half Moon was built as a Dutch present to the united States, designed by my far predecessor F. Baaij working for the Rijksmuseum Amsterdam and built a year earlier on the navy yard in Amsterdam. It sailed at the Hudson commemoration in New York in 1909. As a result of a lack of interest the ship slowly decayed until she was finally set to fire by some moron, I think in 1934.
In 1989 another version of the ship was built, of which the drawings are shown here above.
Baaij published a small book with his design shortly before WWII, meant for model builders, which probably was the first model builders book in Holland. The conservator who came after Baaij, Herman Ketting also published a book for model builders, Prins Willem a 17th century East India man (1651) in 1980 (and I continued the tradition with my books on shipbuilding according to Nicolaes Witsen (1641-1717)).
Here are the drawings from Baaij's book, so you can compare the first and the second Half Moon. Sorry for the low resolution, I don't have any better. Personally I prefer this 1909 version, although it certainly would not have been my design .