Use a systemic mechanism of learning (a bias towards data)
The purpose of Mapping is not just to create a Map and enhance shared understanding, it is also to learn about climatic patterns, doctrine and context specific play. Maps provide a systematic way of doing this as long as you collate, review and learn from them. Having a bias towards learning and the use of data (as opposed to assumptions, gut feel or whatever is popular in the Harvard Business Review — or advocated by McKinsey) ensures decisions are made in a consistent way.
To make your learning more systematic consider creating a Spend Control team, who will become the most important team in your future transformation (for an example of how a Spend Control team works in practice see here.