You're already measuring the lethality of the suicide method in the reviews you cited, because the studies involved measured actual suicide rates and not attempts. So let's not double count any effect or handwave away any failure to show an effect based on dubious logic.
> two of which also proved a positive effect on overall suicide rates
Another way to put this is that four of six studies failed to show an effect. ;) The language "proved" here is a little loaded compared to what's usually used in meta-analyses and systemic reviews for this exact reason.
> "While firearms are used in less than six percent of suicide attempts, over half of suicide deaths are with firearms."
One way to interpret this: people who choose to commit suicide spin a roulette wheel to pick suicide method (or pick whatever is convenient), and the people who pick firearms die more.
Another way to interpret this: people who are more determined to die choose more lethal suicide attempt methods, implement them better, and then die at a higher rate. Firearms are one "more lethal" choice.
Truth is probably somewhere in-between... Everyone knows that hanging is a lot more lethal than overdose attempts, and is roughly equally convenient/available. Including the people committing suicide.
We can even see e.g. research has shown that people who attempt a more lethal method and fail are more likely to successfully commit suicide later-- even when the later method is different.
In any event, I do not really like banning things to avoid possible damage people might do to themselves with those things. There's all kinds of things we could get rid of that would cause a big, clearer improvement to public health at a cost to personal liberty (cigarettes, motorcycles, fast food, processed meats, poutine, etc)...
It isn't really, because we have lots of other evidence to show that reducing access to means and methods is useful.
Mann JJ et al(2005), "Authors identified 6 studies that have demonstrated a decrease in firearms-related suicides after introduction of firearm control legislation, two of which also proved a positive effect on overall suicide rates without substitution of methods (in Canada and the USA"
Lambert MT, Silva PS(1998) "This review concludes that reducing the availability and accessibility of firearms appears to decrease firearms-related suicide rates without this leading to substitution of means of suicide"
There are others.
But let's assume that method substitution does happen immediately: that's still a good thing, because it means that fewer people will die.
"While firearms are used in less than six percent of suicide attempts, over half of suicide deaths are with firearms." - Miller M, Azrael D, Barber C. Suicide mortality in the United States: the importance of attending to method in understanding population-level disparities in the burden of suicide. Annual Review of Public Health. 2012;33:393–408.