I like your approach and have found that a mix of big picture and focused works best for me. By this I mean that first, take your co-workers through the entire process from start to finish, giving a high level description of each area/step and what it does for the final product. Then, since you've already identified the problem, have them focus on the function(s)/step(s) in detail. If possible, allow them hands on performance of the step themselves. Have them speak with the employee who normally does the step day-to-day as they know the process best and often have suggestions for improvement but may have been hesitant to speak up. From there, your co-worker should have a pretty decent idea of "who does what to who" and why things are done the way they are. Then, working with the functional employees he can help them develop a better process flow. If you get a teaming environment established, your employees who do touch labor will more readily take ownership of their processes and will be open to further improvements (change management) down the road.
Hope this helps,
I agree that involvement by the people who actually do the work is absolutely critical to the success of any improvement process, not only do you get better acceptance of any proposed changes but you also get to tap into the expertise of the people who know the process best.