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This isn't a walk report, just to help people find the start given that the usual route is closed at present (late September 2021). This wasn't clear to me from the main route description.
At the top of Upper Mill Street, there is a little bit of a park with the main path up Mill Glen - as described in Stages 1 and 2 - starting to the left of it:
Do not take this! Instead, take the track that is indicated to the right:
and after 100 metres or so the path to Ben Cleuch diverges and ascends steeply to the left:
This climbs up and over the spur east of Mill Glen, then descends into the glen. This rejoins the published route to cross the small wooden footbridge mentioned in Stage 3.
Hope this helps someone!