Could you possibly upload the picture you have? I lived near this bit of Stockport Rd for over 30 years (1960 onwards I'm afraid, but you never know, I might recognise something).
I think that many years ago, Stockport Rd numbers for Longsight ran from Ardwick to Matthews Lane (the Longsight/Levenshulme border), then started again. At some point, Levenshulme lost its own set of numbers and the whole of Stockport Road was numbered from Ardwick to Stockport itself.
Odd numbers on 'modern' Stockport Rd are on the east side, that is the left hand side if you're driving south from Manchester to Stockport. I have a 1970-ish A-Z of Manchester which gives number 689 at the junction of Stockport Rd and Slade Lane. If the numbers for that section of road were the same pre war, then your furniture shop would be somewhere near what used to be Woolworths and is now, I think, FarmFoods. On a modern map, look between Stanley Grove and the railway bridge over Stockport Rd, it's around that area - near Slade Lane, where your other shop was. A lot of that stretch of road was pulled down around the time the Asda was built. I think the Spring Bank pub is still there?
Ooh nostalgia, it's lovely! I have 2 local history books by Gay Sussex on Longsight & Levenshulme. I'll have a quick look & see if your shop gets a mention.
Barbara