In 2004 I was denied a MMD card because I had received a speeding ticket (35mph in a 25mph zone) in 1968 (that's 36 years earlier). I had paid the fine and never had another speeding ticket in my life. My driving license was not suspended.
I appealed the decision on the MMD card. The Coast Guard told me that if I wrote a very long and sincere letter to them, describing how I had rehabilitated myself since my highly dangerous activity in 1968, then had it signed by a Judge or Notary Public, they would reconsider the decision.
After a few months of consideration, the Coast Guard approved my MMD card.
I suspect that you will have a more difficult time than I did.
You may be asking yourself, “What is a Z-card? Do I need it?”
Under Title 46 of the U.S. Code of Federal Regulations, a Merchant Mariners Document, or Z-card, is mandatory for employees working aboard U.S.-flagged ships. It is administered by the U.S. Coast Guard.
Every employee working under the NCL America brand is required to have an MMD Card (Z-card) because NCL America ships sail full-time through the Hawaiian Islands. You will need the MMD card prior to working on one of NCL America’s ships.