Overcontoured crowns. What is the best way to fix the problem? Polishing the crowns?

I've been having inflamed gums above my permanently cemented anterior crowns (zirconia core & porcelain layers) for months. I've been told by several dentists that the cause of the gum inflammation is: the crowns are overcontoured (crowns are bigger than the under teeth) and/or not smooth. I'd like to know what is the best way to fix the problem besides remaking the crowns: 1) polishing the crowns? any risks/cons? 2) keeping the crowns clean with special cleaning tools? 3) else? Thanks!