Doc - perhaps a little basic but is the power steering reservoir topped off with fluid? Is the trouble usually on cold startup? Are there any kinked lines to the steering cylinder especially the long copper tubes where the hoses attach to the steering cylinder?, they are in a rather vulnerable location when backing up in brush? Belt slipping on the pump?
It sounds to me as if the steering pump isn't getting enough fluid and causing the symtoms you describe. Good Luck and let us know what you finally find.