How does traffic handoff between ZMA and Cuba work?
After some searching, I found a paper from Wikileaks from November 19th, 2009, that reads in part:


  
  (SBU) SUMMARY:  Miami and Havana air traffic controllers 
  signed a letter of agreement (LOA) on November 12 updating 
  procedures for the coordination of flights between Cuban and 
  U.S. controlled airspace.  Both sides stressed the excellent 
  working relationship between the Miami Air Route Traffic 
  Control Center (ARTCC) and the Havana Area Control Center 
  (ACC).  The U.S. delegation agreed to review information to 
  be provided by the Cuban delegation regarding flights 
  operating under the rules of "due regard" that could pose a 
  safety risk.  Both sides also agreed to discuss switching 
  from verbal to electronic flight data sharing, on the margins 
  of a regional aviation meeting in Miami in May 2010. END 
  SUMMARY 
  


Apparently handoff procedures have been a regular occurrence for a long time, and are cooperated on extensively.