You can't simply "control" for it, the additional propensity for crime that exists when someone is raised or lives in these conditions isn't something that can be perfectly quantified at the end of the day.

It doesn't need to be perfectly quantifiable for statistical methods to work. If you say the gap is largely attributable to poverty, education, and unemployment, so long as an accurate (if imprecise) measure of these things exists, this theory is testable. Otherwise, you're stuck moving the goalposts, pushing the hypothetical race-neutral source of criminality ever deeper into the miasma of urban poverty where it can live forever, unfalsifiable.

This gets to an important question - who has the burden of proof? It's possible that there is some latent cause of criminality that isn't captured by any of the usual suggested measures, but the position you represent seems to assume such a force must exist somewhere, even if it can't be found. To that, I would ask, why would we so strongly assume equal tendencies towards violent crime as a constraint in the first place? There's no reason to assume equality for any reason beyond its use as a null hypothesis.

Combine with the fact that there's 50 states of data all with different measurements and definitions for race, its a mess.

Again, these are usually solved problems. First, you yourself can do the basic statistical tests - take a uniformly defined and reported measure (e.g. homicide from a Federal dataset) and consistent demographics (U.S. Census for race, Dept. of Education data, etc), and start running regressions. This avoids much of the inter-state problem.

Second, researchers are clearly aware of inconsistent data as a source of trouble, which is why social science is constantly getting better at unifying datasets, eliminating biases, and creating entirely new databases for their research. Objecting to the use of these typical methods and data sources would force you to throw out not just the race/crime unpleasantness, but much of the economics and social science research of the past half-century. Data can always be improved, but simply stating that the data isn't a good answer to this discussion. Remember, people on your side of the issue are using the exact same tools to try and disprove my view.

But what is your explanation, that non-white races are just inherently more prone to murder than whites

Yes.

by virtue of their race?

No; "race" as a category cause things. Similarly, males are unambiguously more inclined towards violence than females on average, but it would be imprecise language to say that they are more violent "because of their sex". That's an unhelpful framing.