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

Pictures would be very helpful as there are several possible causes for gum inflammation. They include ( in no special order) 1. Lack of proper oral hygiene- brushing/flossing and regular professional cleanings 2. Improper or overcontoured / bulging crowns - your dentist must properly shape the underlying tooth to receive a proper thickness crown that results in a crown the same size as your original tooth AND the dental lab that fabricates the crown must create  a replacement crown of proper contour & thickness 3. Open or incompletely cemented / seated crown margins allowing bacterial growth  4. The most overlooked and common cause-  a violation of "biological width" or placing the edges of the crown too far under the gums. This causes permanent gum inflammation unless corrected. Grinding polishing or altering the existing crowns are  not an effective option. Zirconia with layered porcelain can be a fine restoration with a skilled dentist AND dental lab,  and there are still other esthetic ceramic crown options you should discuss. A thorough periodontal or gum examination is in order to first determine the source of the bacterial infection before replacing the crowns.

It would help if you send pictures. Zirconia is a ridiculously hard material that I would never use for anterior teeth.I doubt that grinding and polishing  for a better contour is a viable treatment. I would say that you simply need to have them removed and re-made with a more suitable material.