""Instead, we run a pay evaluation process internally, including feedback about the value of the role and the person from all the people who interviewed the candidate. We publish all that feedback, as well as the suggestion/reasoning of our pay trustees (a group of people who use that feedback to try to place the candidate on our pay scale)""

Problem with this approach is that inevitably part of the formula is also "level" -- so you just converted one problem (negotiating $) to another (negotiating level.) That is when the real tricky people come in -- those who want a high level and just manage others, often adding no value (good managers add a lot of value, but if you tell people that the only way they can make more money is by being manager or senior managing level, then you force people who should not be managing into managing roles.)