Isn’t it ironic that what might actually be needed to address variation in your process is variation in your team?
Picking the right team members is almost as important as picking the right project. In addition to an expert, a customer and representatives from other key stakeholder groups, you should think about how you can “mix it up a bit” by selecting some team members that can bring a fresh look to things. Sometimes a newer employee or someone not directly involved with the process can fill this role. Their view and perspective may keep the team from developing a “group think” mentality by asking “why” to the “always done that way” aspects of a process. Their lack of emotional attachment to the existing process and their distance from inner-group politics sometimes provide them with the courage to bring up the unspeakable, approach the untouchable and refuse to pay homage to the sacred cows. And yes, these differences may create some disagreements and team challenges. An experienced team leader will be needed to help the team capitalize on these differences in a way that brings positive energy to the team.
Different people with different backgrounds and different viewpoints may be just the thing you need to find a different solution to an age old problem.