You are requesting how to do a culture change, better thought of as an organizational transformation. There is too much to say about this topic to keep within the 1900 character limit. Send me your e-mail address and I will send you a set of 6 articles I wrote on the topic entitled "Beat the Odds: How to Beat the 70% Failure Rate of Organizational Initiatives"
- Don't approach it as a "change", which inherently invalidates the current perspectives and people. This will only cause "resistance to change" and the anxiety of which you spoke.
- Instead, create a future (better if they create such a future with the leaders) that is highly desirable and includes the goals you want to achieve.
- Work backwards from that future to the present, including what behavior is needed to fulfill that future. Since behavior is correlated with mindset, this will imply a mindset alteration without dictating one.
- Teach them the skills needed to be successful in the new future (they will now want such training).
FYI, this is the process we have applied many times, including the organizational transformation we led at NASA's Jet Propulsion Laboratory, when a mindset change from command-and-control, hierarchy, no cost limits, and analysis to leadership, team, tight and rigid budgets, and breakthrough thinking was required to implement the low-cost missions that were planned. The recent successful Curiosity mission to Mars (when they talked team, team, team) was one of the results.