Out of the 5 components (St. Nicholas Abbey, Morgan Lewis Windmill, Newton Burial Ground, Codrington College, Mount Gay Historic Distillery), I visited the first 4. In my opinion and experience, this proposal has high chances of getting inscribed on the World Heritage list. 

Barbados was one of the prime British colonies in the Caribbean and has been widely accredited to be the birthplace of rum, a product of the sugar plantations on the island. The sites proposed tell the story of this sugar and rum production in the Caribbean, in my eyes more than sufficiently. 

St. Nicholas Abbey (which was never a place of religion, but rather a plantation), Morgan Lewis Windmill (the biggest and only surviving sugar windmill in the Caribbean) and the Mount Gay historic distillery (the oldest continious rum distillery in the world) are all relatively close to each other, on the north(-east) side of the island.

Entry to St. Nicholas Abbey is 20 USD, but can be upgraded with a tour on the new Heritage Railway to a total of 40 USD. I think this is quite steep, but tourist attractions in Barbados have high entry fees in general.

The Morgan Lewis Windmill was a cool site to visit, especially for a Dutchman. However, the site is quite small as it comprises only the windmill. I did not go in, but the surroundings made it a worthwile visit. 

I did not visit the distillery, as I already has visited the distillery at St. Nicholas Abbey, and seeing as the entry fee to the Mount Gay distillery is very high. I guess I will save this for a second visit to the island. 

The Newton Burial Ground is very remote, located near the more popular town of Oistins (famous for its fish fry). This was the burial ground for slaves of the Newton plantation, and has provided archaeologists with uncomparably rich information on the daily life of slaves in the Caribbean. 

Codrington College, located on the east coast, is also quite remote, but definitely worth the trip. It is the oldest seminary in the Caribbean. The views of the Atlantic and park surrounding the seminary make this visit even better. 

If sites of tequila production can make it to the World Heritage list, so too can the sites related to rum and sugar production. In general, the selection of the sites provides a very good view of the role (slaves in) Barbados played.