Hi, nice looking analysis. I would work a bit on the map projection (although understanding map projections is easily a few weeks study!). Maybe something like:

GeoRegionValuePlot[
    ...
    GeoProjection -> {
        "LambertAzimuthal",
        "Centering" -> ....
    },
    ....
]

Here is a good stackexchange example. Also useful is An Album of Map Projections.

Although I might be misunderstanding your analysis, you state:

There seems to be no correlation between murders by firearms and the gun freedom index.

but, common sense would seem to say with more guns, you get more violence. For example, the following paper states:

While many factors influence the rate of gun-related violence in any state, comparison of these rankings with the aggregate ranking of states based on gun-violence outcomes reveals a significant correlation between weak state gun laws and increased gun violence in a state. Across the key gun-violence indicators that we analyzed, the 10 states with the weakest gun laws collectively have a level of gun violence that is more than twice as high as the 10 states with the strongest gun laws.

Source: America Under the Gun - A 50-State Analysis of Gun Violence and Its Link to Weak State Gun Laws