So then surely you should be able to provide hard data that shows reducing gun violence has a specific and measurable impact on violence as a whole, no?

I would propose that it's entirely pointless to focus on gun violence specifically because it's defined not by what makes it a problem (the violence) but rather by the arbitrary tool involved (guns). You could reduce gun violence to zero, and nothing would be better if the overall violence stayed the same. Which literally all available evidence demonstrates that it would, as you're not the first person to want authoritarian gun grabbing in place.

I don't want any more of this faux "compromise" bullshit handed out by gun grabbers. Our rights have been compromised enough with not a single damn thing to show in return. It isn't a compromise when they just do half of what they want and kick the other half down the road as a loophole they need to close.