As she repeatedly travels back to a Georgia in 1815 from Chicago in 2016, a black woman must figure out how to stop time traveling before a ruthless plantation owner ends up killing her.

Interestingly this sounds almost exactly the same as the plot for Octavia Butler's novel, Kindred, published in 1979 in which a young black woman from 1976 mysteriously time travels back in to the 1800's south.? Have you read it or is this just one of those bizarre coincidences.

Kurt Vonnegut used a similar situation in his classic novel "Slaughterhouse Five" which was adapted into a poignant film. ? ?Vonnegut used the uncontrolled, random time traveling of the protagonist, Billy Pilgrim, to frame a slightly fictionalized narrative of his own experience as a POW in World War II and witness/survivor of the hellish fire bombing of Dresden, Germany. ?

And he used it to frame his theme, that life (and death) just happens, randomly and absurdly.

What's the theme you propose to explore with the time traveling story gimmick? ?What's the point of having a character trapped in a predicament of uncontrollable time travel?

And wouldn't it be a stronger objective goal be to not merely save the life of her 1815 version, but to win her freedom? ?I mean extending the logic of the premise (insofar as I can grasp), if she succeeds in stopping the murder of her 1815 self and returns to the safety of her 2016 self -- couldn't the 1815 version still be left in the lurch, enslaved?

I like the concept. You should check this movie about two brothers?who are sent back in time to 1780 Antilles as slaves.
http://www.allocine.fr/film/fichefilm_gen_cfilm=182097.html
This movie presents a clear inciting event: when they tear up the 'freedom?document' inherited by their grand father they are punished by a witch who wants to teach them a lesson. It's celarly a comedy.
In this movie they travel from France to Antilles at the beginning to collect their grand father will.

What it's interesting here is that this movie addresses the two issues pointed out in the previous comments here (space travel and inciting event).