While I too have not tried rolling out EOS in this large of an organization, I have worked with companies who were rolling out agile project management practices in a similar fashion. In this case they created Scrum of Scrum teams for each region and had a member of each on a similar global team. So basically global leadership and maybe even department teams, that have a representative also in a regional L10 who also has a representative down in regional departmental L10s. You want to have traceability between each level of teams, whenever you get a break where a team doesn't have a representative in a higher and/or lower team breaks in communication and alignment occur.
Jason C Roelofs
Next Level Software Leader | COO - EOS Integrator for Xeo Software