I am Yorkshire born (which is obvious from my name) and my family goes back many centuries. I am thus more qualified than most to speak on behalf of my county.
What the OP wants is anthem-like pieces (such as Trelawney) and the Holmfirth Anthem seems eminently suitable for Yorkshire. Equally so would be Spencer The Rover which Robin Dransfield recorded with a brass band accompaniment.
Either must be better than any Green Howards military march anyway (especially as the Howards nicked our ancestral pastures).