For the sake of this chaotic journey I don't suppose exact locations were critical; or even all the better for being all over the place!

Pin Mill Brow is on the River Medlock over to the east of Piccadilly.

* Bailey Bridge
Yes, according to CanalPlan maps
New Bailey Street Bridge ('Manchester Ship Canal (River Irwell Upper Reach)')
 is at New Bailey Street\Bridge Street West(a continuation of Bridge St, not picked up on googlemaps except on streetview)
https://canalplan.uk/place/kp2q

† Throstles Nest Footbridge is on the Bridgwater, west of Pomona
Stretford, Manchester M16 9FG
https://maps.app.goo.gl/3hHhwNXYwttZ8sgK7