Thank you for posting this.  I remember this from college.  It is not well known that the south had slave patrols and some of the southern colonies were police states.  The southern states wanted to be able to raise militias to protect against slave up risings.  They were afraid from day one of a centralized federal government.  

The world is a complex place and anytime you try to narrow it down and simplify it you're usually wrong. Were there some southern politicians that pushed for the 2nd amendment in part because of slavery? Probably. But it was just one reason and probably not the most salient.

100 years before the American revolution some Catholic English king attempted to disarm the protestant population. The right to bear arms was written into English law at that time. Nothing to do with slavery. Many of the colonies were begun by those same protestants fleeing oppression from England. Those religious colonies remembered that attempt to disarm them. Some of those protestant northern states wrote that same protection into their state constitutions based on that English law. States with so few slaves that insurrection was not even a remote possibility.

Militias were not an exclusive southern phenomena whose main purpose was to put down slave rebellions. Most northern states with virtually no slave population also had militias whose main purpose was to fight indians. Just a few decades before the American revolution northern militias fought the French And Indian war.

One can plausibly make the case the the 2nd amendment was just because of slavery or just because of the recent rebellion against a tyranical crown or just because of the need to fight Indians or merely a continuation and extension of freedoms granted under the English bill of rights. I think its all of those. But imo our American freedoms fit most neatly in a historical context that includes the steady increase of rights in England.

It is true that changing the language of the amendment favored the Southern States.

But  the change should be seen in the larger context of the idea that militias could replace the function that armies played in European States. The colonies (a very fractured collective whole) just won a war against such an army by organizing militias and not needing to organize all of them. The making of the Constitution was done with the hope that the evils of standing armies could be avoided while still enjoying the benefits of a unified polity.

In Federalist Paper No. 29, Hamilton dismissed the fear expressed by unnamed parties that militias from one group of states could take action against another under the name of national security. The language of the Second Amendment does not address this problem. Nor did it provide a stumbling block to exactly that action taking place with the outbreak of the Civil War.

Another element to take into consideration is that the South had cut a very sweet deal with the 2/3rd rule of representation letting slaves be counted as citizens that provided a lot of power on a Federal level. Their point of view obviously changed with the abolition of slavery and crushing defeat of their economy.