Your best options ex-MIA would basically be via CUN, or Canada with Air Canada.
Cubana are notoriously unreliable, so allow plenty of time at each end of your connection into/out of HAV. Also factor in weather (hurricane season) depending on when you plan to travel.
Via MEX is also an option I believe.
We flew MX ex-CUN which of course is no longer an option......
if you search, there's quite a few threads on best ways to/from cuba.