The most likely way the Great Migration would have been prevented is if the southern landholders – who had regained absolute control over the black population with Redemption in the 1890s – had been successful in preventing labor scouts from recruiting blacks to move north. Quite likely, this would have meant industry moving to the South, with extremely strong laws to keep the races separate in new industries.
Alternatively, another possibility continued black residence in the South would be a successful Reconstruction. The whole reason so many left was because Reconstruction failed and allowed Jim Crow laws to take over. If the Radical concept of '40 acres and a mule' as well as protected voting rights, the South would become an attractive region to black people.
I've been weighing writing an Alt Timeline where the PoD culminates in a completed radical/redistributionary Reconstruction. It's probably not election centric enough to work on this forum though.
I think depending on where the PoD is here that stops the Great Migration is strongly affects the material conditions and political dynamics of the South in the hypothetical 2016. I honestly have no idea what would have happened if, in a sense, we gave Jeffersonian Democracy a chance to air itself out in an entire region of the country by redistributing most land to create a small-plot yeomanry. I do think that if you engaged in that sort of leveling and, say, included landless whites as beneficiaries of said redistribution, you wouldn't get the reactionary coalitions that re-imposed racial hierarchy whenever cross-racial political coalitions emerged in the South (Reconstruction, the Populist/Fusion era). No Jim Crow, strong black representation in DC, strong foundations of black ownership in an integrated economy, and equalization of class relations all sound pretty good to me, though. I would imagine that depending on how you dealt with the former slave-owning class would have its own aftereffects and impacts on the region.
The other scenario (a hyper-repressive South that sort of turns itself into a hermit kingdom) doesn't strike me as particularly realistic, especially once you get, say, the automobile. That said, there is some amount of precedent even within the history of the region itself (cf: the censorship of abolitionists tracts being distributed by the US Mail in the 1830s. A similar tactic was used during WWI nationwide to curtail distribution of socialist magazines in the Wilson administration) for the strategic suppression of information, so I guess it could happen.
In this scenario, I'm not even sure you *get * a VRA. Or if you do, it's really weak. One of the driving factors (other than, you know, a sense of human decency) driving northern Dems and liberal Reps to pursue civil rights laws was the potential voting behavior of black populations in northern cities. One thing that the Caro biographical series on Lyndon Johnson perceptively notes is that the 1957 Civil Rights bill can in many ways be construed as a Johnsonian (or at least Democratic) response to Eisenhower's actions to enforce the
Brown decision.
If, rather than potent independent actors with national influence, black people and the question of Civil Rights is viewed as some regional curiosity of limited relevance outside the South, and Dems are not forced to choose between northern urban success and the Solid South, I'm not sure Civil Rights gains traction as an issue.
Maybe this leads to more radical/socialist activism on the part of civil rights leaders (without northern liberals to court, the Liberation struggle maybe opts for the Robert F Williams route than the MLK route). But I don't know how it develops from there. Especially given that the role that the Cold War played in affecting Civil Rights discourse (anyone who advocated for any sort of change in the South was labeled a Communist in REAL LIFE, much less in this timeline, and racial violence and hierarchy was a black mark on the US reputation throughout the world), there are just too many variables to consider on that branch.
But again, I just don't see (once you have trains and cars and radios) how you keep people from just *leaving*. Especially with the policies that theretofore had kept people there.