Because of the nature of criticality, no amount of traditional "training" or additional bureaucracy/procedures can fix this problem, it requires a new approach to give an much better intuition of the dangers, PLUS some new safety gear that is always giving feedback to the wearer when things go bad, along with networking/surveillance.
First - They need a VR/AR training system that shows danger levels visually, audibly, and via any other sense that make the user instinctively aware of what they're getting themselves into. In training, they should go through all the ways you can die, just like pilots do in simulators.
Second - There needs to be new safety gear that is an interactive, networked, set of sensors to detect radiation all the way from alpha through fast neutrons, and gives immediate feedback anytime things start to go south to the user. It should also warn everyone immediately in a criticality event.
Think of it like you would the explosive gas detectors that coal miners use, but more powerful/integrated into the network.
There should be very strict rules about the access of the data gathered, to ensure people feel it won't be abused for normal office politics, etc.
Third - A management system that catches the failures in safety, and discusses them, and a rate of zero failures/year is obviously unobtainable, and should also be unacceptable. There are always mistakes, they need to be caught.
Fourth - Everyone who works in criticality related materials should be required to have a will, advanced medical directives, and recorded preferences about euthanasia signed and witnessed, to stress the ultimate danger.
Fifth - Psych screenings (One would hope they do this, but probably not)
Sixth - Review these things every 5 years.