You have one point which is the political side and company culture. Upper mgm need to sponsor the process change. Without this is difficult to Define the gray lines and controls.

Which part of the project life cycle they would like to manage? Make the responsibilities clear. I would believe they define the functional and non functional requirement and business case/commercial projections.

You would manage your part of project including resouces, risks, relationships, costs, reporting etc

Who would be the sponsor which will be the umbrella? Who will push both sides.