I'd enjoy some stats that show a reduction in gun ownership and/or a raise in registration/NICS checks that have a relation to a reduction in violence violence, and not just gun violence. South London is one of the most violent places in the free world, more "hot" home invasions than anywhere in the US... but guns are illegal there.
Regardless of what spiked deaths in Missouri, this did in fact coincide with the entire gun-owning conservative South buying up as many guns and as much ammo as they could find. There's still a shortage of it, as far as I can tell. They did indeed do this because of liberals entering office who would of course immediately 'snatch up all the guns' (though they did no such thing). Though not necessarily because of the guy's skin color. Of course whether or not they are directly related remains to be shown by the evidence given.
Obama's administration charged the Center for Disease Control, after Sandy Hook, with treating firearms violence as a disease and studying the consequences. The CDC reported back with gun death (suicide + homocide) averaging 36,000 per year, while justified self-defense shootings average possibly as low as low as 60,000 per year, with an upper limit at 2.5 million (though this specific high number has other assumptions made, and is less accurate) self-defense gun related scenarios.
Levitt, who I earlier mentioned, also shows with pretty strong evidence that even with the Clinton Assault Weapon ban of the 90's, the drop in crime that happened subsequently, had more to do with Roe v Wade 20 years earlier, thus curbing the 20-something year old criminal crowd that would been coming of prime criminal age in the 90's; than actual gun control laws had to do with the drop in violence/crime. Note that in his thought experiments he attempts to correlate gun control with curbing violence, not solely gun violence which gives erroneous results always in favor of gun control... even if more people were killed that year overall.
Once again, Obama and the CDC's firearm study (which I recommend googling and reading), is possibly one of the most comprehensive studies done on US firearm crime/violence, and they seem to conclude it's about split, with the necessity for more future data. I noticed conclusions drawn from that report were quoted in the OP, I thought it'd be fair if self defense part were mentioned as well.
IMHO, I trust Brady Campaign stats about as much as I'd trust NRA stats on the same subject, which is to say not at all.