Ban the sale of new high-powered firearms and handguns, and sunset the legal registration of existing ones alongside a properly funded, non-mandatory government buyback scheme.
Base subsequent changes to the balance of incentives on measured and publicised changes in public behaviour.
Basic restrictions on gun ownership would create immediate difficulties for many of these "lone gunman" attacks. Despite the flood of registered and unregistered guns in the US, it's not as if people like Elliott Rodger or Dylann Roof are so well-connected they'd be easily able to obtain powerful firearms if they were made illegal.
Strikes me the biggest problem with policy change in this area in the US is that once implemented, the GOP would make it their mission to repeal gun control.