My go-to for getting a sense of the empirical literature on some issue is to look for review articles that aggregate the results of multiple studies. I found this review, which suggests that there is a correlation between gun prevalence and homicide (and not just firearm-related homicide). The article is gated, sorry, but here's the abstract:

This article reviews the most commonly cited, representative, empirical studies in the peer-reviewed literature that directly investigate the association of gun availability and homicide victimization. Individual-level studies (n=4) are reviewed that investigate the risks and benefits of owning a personal or household firearm. The research suggests that households with firearms are at higher risk for homicide, and there is no net beneficial effect of firearm ownership. No longitudinal cohort study seems to have investigated the association between a gun in the home and homicide. Two groups of ecological studies are reviewed, those comparing multiple countries and those focused solely on the United States. Results from the cross-sectional international studies (n=7) typically show that in high-income countries with more firearms, both men and women are at higher risk for homicide, particularly firearm homicide. Time series (n=10) and cross-sectional studies (n=9) of U.S. cities, states, and regions and for the United States as a whole, generally find a statistically significant gun prevalence–homicide association. None of the studies prove causation, but the available evidence is consistent with the hypothesis that increased gun prevalence increases the homicide rate.

And here's the conclusion:

The available evidence is quite consistent. The few case control studies suggest that households with firearms are at higher risk for homicide, particularly firearm homicide. International cross-sectional studies of high-income countries find that in countries with more firearms, both men and women are at higher risk for homicide, particularly firearm homicide. This result is primarily due to the United States, which has the highest levels of household ownership of private firearms, the weakest gun control laws, and the highest homicide rates. Time series studies of particular cities and states, and for the United States as a whole, suggest a positive gun prevalence-homicide association. Finally, perhaps the strongest evidence comes from cross-sectional analyses of U.S. regions and states. Again, places with higher levels of gun ownership are places with higher homicide rates.

None of the studies can prove causation and none have completely eliminated the possibility that the association might be entirely due to reverse causation or omitted variables. But the available evidence is entirely inconsistent with the hypothesis that increased gun prevalence lowers the homicide rate. Instead, most studies, cross sectional or time series, international or domestic, are consistent with the hypothesis that higher levels of gun prevalence substantially increase the homicide rate.

I haven't read through the study you linked, and it might be the case that the methodology in that study is significantly more reliable than that of other studies on this subject. If you are aware of an argument to that effect, I'd be interested to hear it.

One of the best attempts I've seen (and not just because it happens to support my position, I swear) is this study from the Harvard Journal of Law & Public Policy.

What are some of the non-best attempts you've seen?

I agree that it is important to look at homicide rates rather than rates of gun deaths. (Relevant) arguments against gun restriction are basically that, first, it isn't practical to significantly reduce the amount of gun ownership amongst the prone-to-impulsive-violence population, and, second, that if you did other deadly implements abound, especially ones that magnify strength disparities that likely correlate with being violence prone.

Looking at just gun death rates after restriction can argue against the first (given other variables controlled) but murder rates are the more important stat and could update both hypothesis one way or another.

This is interesting, but correlations of such generic variables without a clear causal story to explain them are a bit suspicious: there are so many confounding factors. How does gun possession reduce homicide from other causes for instance (Deterrent effect? Dubious since most homicides are heat-of-the-moment crimes of passion). How does gun ownership reduce suicides?

The original poster asked for evidence on a par with "smoking causes cancer", and this Harvard study seems a lot like comparing smoking rates in a country against overall death rates in a country. (There might well be a negative correlation there too e.g. if countries with more smokers are generally more developed and so have lower death rates overall).