Dunphy might have corrected himself on another map - or got it right on another. Heh.
This reminded me of Fox/Keats, looking it up in their Upper Grose book they say that Arethusa Falls is so named because Alpheus married her in Greek mythology (which fits the end of the canyon bit, where the 2 canyons meet). They also say the falls are mentioned in a newspaper in 1897.
Well, i found it.... it's a list of local attractions and it appears to suggest access - I'm guessing to view- via Medlow, with Minnie Haha on the way from that side:
https://trove.nla.gov.au/newspaper/article/194839609Makes me wonder if again, they were looking at the "real thing" - a pretty long trek out along Carne's perhaps? Don't even know if there is a good vantage point out that way - or if they were actually referring to our phantom set further up Katoomba Creek.
Ah! Here is a Tourist Map from 1912, which shows how they would have access "Arethusa falls" - again, it's at the junction of Katoomba/Govetts:
https://collection.sl.nsw.gov.au/digital/oAlQkkW3kAR2DNot only "Arethusa", but also, "Good Camping Ground" at the junction of Greaves/Govetts! Firming up as the spot for Syncarpia, even if it is now quite overgrown/flood affected. But isn't that interesting, access from the Pt Pilcher rd, then working up the creek to see the falls.
And for good measure here's a map from '35, showing Arethusa again up at the Katoomba/Govetts junction.
https://collection.sl.nsw.gov.au/digital/6v6602mAqkZ0gI am starting to think the set at the beginning of the canyon was the original - that's several pre-Dunphy references now to that spot, plus him as well. And in common use, due probably in part to Dot and co's exploits going up it, the falls at the end of the canyon ended up with the name.