A lot of the discussion around untying pay to performance is still largely induced theory, softly correlated to some evidence. Definitely there are some strong arguments to consider, but plunging into this school of thought is quite risky.
If you want to approach a single salary level or a very small range perhaps, I would not shoot for any salary level that already exists in your organization. You still have the ongoing problem of attracting new talent and mitigating existing talent from leaving. Therefore, I would analyze the market and establish the range and frequency distribution for a particular job family, then establish a salary target on whatever percentile makes sense for my organization, a value that will still attract new talent from my competitors.
For example, if you discovered that for job family A the salary ranges from $31K to as high as 65K, the MODE is say $52K. I might choose to be in the 80th percentile which would put the salary around $55K.
Setting the target based on external actual data will level set everyone's expectations, be a standard set from reasonably objective data, and remove any sense of unfairness.
From there, I would begin a program to start moving people towards that value, either in increments or in one move. I would NOT move higher paying people towards that value. That would have to change through attrition.
If the proponents are right on this, this method could cure those internal issues they cite; however, I cannot see how you would remain competitive in the market place when finding talent. The market, supply and demand, is dynamic and in constant flux. This single salary method will, in my view, completely disable you from being agile enough to respond to changing market demands. If it becomes a buyers' market, you would end up being the highest salary provider and that will make you too expensive to compete for business. If it becomes a sellers' market, you would become the lowest salary provider and you will lose all of your talent and attract no one.