We just came back from a holiday in Europe, including a couple of weeks in Greece. While we were in the town of Archea Olympia (the original site of the Olympic Games - an absolutely stunning archaeological site), we came across a privately run "Archimedes Museum", which features working models of examples of ancient Greek technology - including a working Reconstruction of the Antikythera machine.
https://archimedesmuseum.gr/en
http://kotsanas.com/gb/exh.php?exhibit=1301001
The museum is founded and operated by a Mechanical Engineer, Konstantinos Kotsanas, so while there might be an element of hypothesis / imagination in some of the reconstructions, they are all based upon sound engineering theory, and a good understanding of ancient Greek technology.
He also runs the “Museum of Ancient Greek Technology” in Athens, and the “Museum of Ancient Greek Musical Instruments and Toys” in Katakolo, but we didn't get to those.