Miami to Havana: direct flights?

Hi Cuba Travel Experts! We are Americans (husband is a newly minted American citizen originally from Cuba) and we are applying for an OFAC license for family travel to visit my husband's mother and other family in Havana. We know Cuban-Americans can fly non-stop from Miami to Havana, but how do you book those flights? We called the airlines and none would admit to flying to Havana! Do we have to book through one of those special South Florida travel agencies, like Marazul or Tico? Has anybody out there used one of these agencies? Which are the most reliable and cost effective? Are there any to avoid? Any other suggestions to make this highly- anticipated trip easier? We're all so excited and want it to be a great experience, obviously. Thanks in advance for your advice...
 
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Miami flights