It occurs to me that the best way to more actively police and enforce responsible gun ownership is to 1) promote respect and education for firearms, and 2) promote gun-owners having a stake in the welfare of other gun-owners.
Propose legislation wherein future gun ownership is dependent on having passed a certification process, as well as requiring sponsorship of other gun owners before a firearms purchase or registration can be completed. Sponsors should be at least partially liable for the actions of those they sponsor should law violations occur involving firearms.