I have the same type of clay, Pressure washer not much help. I have found it best to park the tractor for a day and let the goo dry a bit, crumbles right out of the tires next time you move the tractor... Both r1 and r4 tread
My stuff turns to a kind as I describe it, 'adobe' kind of orange/tan concrete after being cooked under a brush pile fire.
Makes the best ball and burlap dug trees. It holds moisture like nothing else and the dense clay really helps avoid root disturbance, 'makes clean cuts on tree roots' when dug. Alfalfa and clover loves it too....