A Wicked Situational Study
You are unlikely to come across anything as gnarly as the project situation with which you and your team is now faced, but embedded within are several lessons to help you gain confidence! You are on the right track, from what I have seen. Remember that we dare not plan just yet. We will work together to learn how a Project Manager - who, unless he or she is blessed with charisma - earns respect and authority from the earliest project phases.
We actually need to clarify and manage the expectations of our sponsor first, to protect the deliverable as stated.
By the way, next Monday I am welcoming a recruiter to launch the class - I try to afford students opportunities to consider potential opportunities so close to graduation. I also have invited a former student for another time, to discuss her roles and responsibilities, and challenges, managing multiple projects.