I think we agree that some counties with regional associations go much further north and south than those links suggest. Lincolnshire, Nottinghamshire and Derbyshire are midlands counties in most people's eyes, but in their upper reaches have cultural, industrial and regional accents that are indisputably northern. Nottinghamshire has Finningley at the top, which is way into Yorkshire latitudes, more northerly than many unarguably "northern" places, and Normanton on Soar in the south which is firmly in the bucolic, cheese producing Leicestershire Wolds.
Cheshire is an anomaly, as someone from Newcastle upon Tyne or Penrith would see it in a midlands context, but as a dormitory county for Manchester its links are to the north. My barometer of the south is when the terracotta bricks of the midlands turned to the yellow ochre bricks of London from the train window.