My years of experience have prepared me well for this marketing role. You mentioned that customer service is a big part of this job; I spent three years working in a high-volume call center, answering customer calls and identifying solutions.
I developed extensive skills in working with customers, even when they were distressed. I'm excellent as deescalating situations and finding a way to make the customer happy. Since the role of your marketing department is to improve customers' impressions of the company, my experience will be an asset to your team.