This is a bit tricky because at any one time Stockport has come under Cheshire, Derbyshire and Manchester aswell as its own Metroplitian Borough.
As it is Stockport may hold some documents relevant and there is a list of their records here:
http://www.familia.org.uk/services/england/stockport.htm l
There are also addresses of the Cheshire records office aswell on the above link.
Other than that the records in Manchester are at:
http://www.gmcro.co.uk/
they are very strong on family histories there and hold many records relating to Manchester's (and the surrounding areas inc Stockport) industrial past.
They are very helpful but you have to be very very specific on what you are looking for. It sounds like you have some good starting points but you will not get immediate results - you will have to do a lot of digging.
The local studies unit at Central Library in Manchester are also very helpful but remember they only hold records for Manchester (who's boundraries have changed a couple of times over the years!) so if your ancestor didnt actually live in Manchester he wouldnt show up.