Something that helps a lot: have a safety incident team with absolutely no connection to HR. They have no ability to fire anyone or report on your performance review, they don't talk to managers about people and just record and compile safety related issues. Yeah, you may have an employee or two who screams wolf a lot, but their job is just to investigate, fix the specific issue, anonymize, and aggregate the reports. This lack of connection should be very public so everyone feels comfortable talking to them.

This is part of how the FAA vastly reduced the fatality rate in GA. They stopped playing cop and started playing engineer.