I enjoyed the show too.
The only disappointing point for me was the readiness with which the programme leapt to accept as fact the (unfounded or at least un-evidenced -- and very probably undocumentable either way) suggestion that the great great grandfather was the illegitimate child of the Antiguan planter. This might make for better TV and a more dramatic story but was not based on proof of any sort -- and proof has to be the foundation of any reliable genealogy (or else I'm a descendant of the queen of Sheba).
The programme also exported early C21th assumptions back into the early C19th. In the era before universal state education, to become a teacher did not usually involve formal courses and qualifications. When the threshold of ignorance was so low, to become a teacher one did not have to rise so very much higher above it. I know this from my own family history, where in the late Victorian era some of my kin in their late teens, without any but the most elementary education, became "pupil-teachers" and later school masters and mistresses. I see no reason to assume that, decades earlier and in the Caribbean, the gt gt gf in the programme had any more structured training to become a teacher (which seemed to be the presumption in the programme).
Nonetheless, it's great Tuesday night viewing.