First, it's essential that your management recognizes that they have a problem, and that they WANT to go to a performance-based culture. It's also essential that they have the leadership skills to get you there. This alone could take a long long time.
Next, yes, I think you do have to change incentives/rewards/pay structures/etc. Currently, managers get rewarded by higher salaries if they have more people reporting to them. So, if they streamline so that they can get the same job done by having the same or fewer people, they are jeopardizing their own pay. That's messed up.
If you do have metrics, yes, you should measure and publish them.
However, not all things can be measured as Caryn says above. For example, I'm a question-asker; I add tremendous value by asking good questions for others to consider as they plot strategy or revise processes. I also have a very wide and fabulous informal network I can tap. These are the single two best things I bring to any job but neither lend themselves to a performance metric.
I think in terms of incentivizing performance, innovation, etc. you have to do management by objective. State the objectives clearly and reward folks who achieve them, instead of trying to count each and every thing. It's not that different from gaining approval to telecommute; some managers resist that because they feel they lose control if they can't 'see' their employee and ensure they're working a full 8 hours - when the point is - are they getting the job done? (all based on setting clear understandable objectives, for an agency, for a position). Critical when you're talking about metrics.