One advantage of fuzzy project objectives is that they let you avoid embarrassment in estimating the corresponding costs. The effort required to correct a project that is off course increases geometrically with time. The longer you wait the harder it gets. Do it now regardless of the embarrassment. The project purpose statement you wrote and understand will be seen differently by everyone else.
Measurable benefits are real.
Intangible benefits are not measurable, thus intangible benefits are not real. Intangible benefits are real if you can prove that they are real. If the project participant has a time conflict, the work given by the full-time boss will not suffer. The greater the project's technical complexity, the less you need a technician to manage it. The manager will get the technicians.