First of all don't merge all of your department's document libraries in to one document library! Since there must be a reason behind the existing structure. For example, two reasons:
security/access - if people have read/write access to documents in their department, that is fine. However, if you use only one document library, the people in e.g. Sales will be able to edit HR and Finance's documents!
document lifecycle - for managing and expiring documents. This is much easier to do when document are split out in to different document libraries.
You'll need to find another way to cope with your management's requirements. The departments can either go to the management site to report on their results or you find a way of using 'look-up' columns to do this. The standard Sharepoint 'look-up' columns are insufficient for inter-site collection work. Does each department have a separate 'site collection'? If so, then I would recommend third party Sparqube look-up columns - I don't work for Sparqube.
The 'look-up extra' column type means you could look up 'project name' and 'progress' fields from different lists/document libraries in different site collections.
Another method would be to use CQWP (Content Query Web Part) to build a sort of dashboard for management to use. The queries you define would display the relevant content for management to review.