One of the most challenging skills for a Project Manager is to plan work for a team, whose members are also working on other projects, so that each resource on the team is optimally allocated for 100% of their available capacity, across the various projects in the portfolio. Cloud P. Consulting can get you there, but consider not attempting this in the first phase of your project.
Perhaps you might start by having project managers centralize their project information in the Project Server, and become familiar with updating their projects regularly in line with the cadence established by your organziation. Help them get into a rhythm and have success in the new solution and start to understand the differences between Project and Project Server through their own experiences.
When project managers are comfortable with updating, saving and publishing their projects regularly, then you might consider the benefits of having team members submit their task progress via Project Server. This will introduce a level of complexity which is unfamiliar at first, but which can be easily managed with the right level of Project Server expertise.