Your approach perfectly makes sense.
- Design the Master Data model as the core piece of the Enterprise Information Map
- Assign ownership of information entities to business units
- Identify "central" information entities without "natural" owner (such as master entities Party and Location as well as reference data) to a (new) central unit responsible to conceive mechanisms for management and governance of "central" information entities and to license the above mechanisms for reuse in decentral business units
- Nominate data stewards in decentral business units that are responsible to reuse central mechanisms and, based on entity ownership, to conceive decentral measures for data governance
- Reorganize business processes based on the above mechanisms as well as to integrate data governance measures
- Restructure existing business units to support the reorganized processes
- Train managers and staff how to support the "new" culture.