If the idea is for the entire labor market to change significantly due to everyone voluntarily sharing their salary, then we ought to be talking about a mechanism of ensuring honesty, just like an auction (generally) wants to design their auction in such a way that people are honest about their willingness to pay.

Ideally, but you do not need the entire labor market to participate to do it. I am guessing even shining a light on a small, representative set of real time data will be enough to get things moving.