Today mum and I took the train two stops to investigate. We found a lovely tidy store packed to the gills with fabric. It hangs from the ceiling and bursts out onto the footpath. The main branch of the store is in Namba, central Osaka. This one is a lot smaller, not at all crowded but surprisingly well-stocked with fabrics and notions.
From the airport it's just four train stops. You could do it if you had an overnight stop-over in Osaka although I recommend the other stores I have written about on Flickr more.