Other countries got on top of their gun ownership problem without door to door goon squads going around. It's not rocket science.
For instance, the rate of household gun ownership in Australia in 1988 was ~24%, which isn't much less than the 31% in the USA.
About 6% of Australian households have a gun now, and no goon-squads going door to door was required.
Similarly, the number of US households with a gun
fell from
50% in 1977 to 31% in 2014. Less people have a gun, now (even if that's offset by one guy with 50 guns) which succinctly explains why gun deaths are down, overall in the USA. Again, where were those gun-grabbing goon squads which are supposed to be an inevitable part of reducing guns? If you say "the ATF", then well, gun owners are not in fact doing a very good job in preventing the ATF from taking other gun owner's guns, are they?
In future years that current 31% will probably head down to the low 20's and you'll have something like 1-in-4 or 1-in-5 households with any firearms, rather than the 1-in-3 now. And that's good: because 80% of households which have a kid who could go insane won't have that kid getting access to a gun, and at that point in time burglars will be significantly less likely to find a gun to steal when they rob your house - note the obvious fact that burglars try and rob your house when you're
not home meaning that self-defense guns are much more likely to be stolen by robbers than used to fight robbers. Very few robbers want a "home invasion" situation because they know it's very likely to turn into a shootout vs the cops.
Again, that's before any laws even need to be passed. People in general are just getting more gun-averse over time, because of all the high-profile shootings. It won't require much in the way of new regulations to cause that number to decline faster, because it's already headed in that direction. A small nudge such as new regulations or taxes, or requiring permits for new purchases of handguns, will cause the number to decline faster.