I would only go thru US......I went alone under general license as an "educator" several years ago. I give occasional tours at a museum. Flew Delta out of JFK, noon flight on Saturdays, returned week later. Picked up brochures from a few art galleries and kept a journal....thats all. Was never asked any questions going thru customs either way.
Would highly recommend Park Central Hotel in Havana . Great location. Used Marizol travel agency, they gave me all kinds of hints to go" legal".