Ironically, not only is the phrase not associated with the slave trade of any age, good evidence suggests it originated here in the U.S., not later than about 1956 and zounds! was a phrase placed into the vernacular by blacks themselves.
Phrase Finders has it on good authority that: "...Where it does come from isn't known. It is one of the many phrases that use rhyming reduplication, for example, namby-pamby, willy-nilly etc....", However the origin is "... has no evidence to support the suggestion that 'nitty-gritty' has any connection with slave ships. It may have originated in the USA as an African-American expression, but that's as near as it gets to slavery. It isn't even recorded in print until the 1950s, long after slave ships had disappeared, and none of the early references make any link to slavery.
There are several citations of the phrase in print dating from 1956, for example, this line from Alice Childress' novel Like One of Family:
"You'll find nobody comes down to the nitty-gritty when it calls for namin' things for what they are."
Another is from the Texas newspaper The Daily Journal, in June 1956 and comes from a piece which gave examples of 'the language of 15-year old hepcats':
"She buys, with buffalo heads, ducks to the local flickers, but they prove to be corny and along comes a nitty-grittygator in a cattle train which she hops."
Unfortunately, the Journal didn't include a translation, but I have it on authority of several US contributors of the correct vintage that, in that context, a 'nitty-gritty gator' was a 'lowlife hip dude' and a 'cattle train' was a Cadillac..."
Lending itself to misinterpretation is that the phrase, in it's fullest rendering usually includes "... getting down to...", hence a possible mistaken application referencing a ship's hold for which the phrase was unjustly excoriated...