I don't think you have gone wrong. I have a piece of paper put together for a Welsh Mines Society visit in 1996, by the late Adrian Barrell, who knew the area as well as anyone. His numbering of the levels matches that in your photo i.e with Pant Mawr mill on Level 10, Fron Boeth mill at level 18 and the Cefnybraich mill and the tunnel at level 22.
There was no level 13 on his map.
The open levels on Cefnybraich are numbered 12 and 13, so not really part of the sequence.