Advanced sum formula required

I would use a completely different design for this data, then generate your summary using a pivot table. You might not like this as much but it is the optimal Excel solution. This assumes that the rate for each staff member is the same regardless of project. I do something very similar to this only with 8 employees and tens of thousands of records and dozens of projects, with a lot more complexity, and it works beautifully. Once your organize your data like this it opens up all other possibilities for analysis.

This is your same data, with one piece of data per row--project, staff, week, hours. Rates are on a separate tab. Report is on a separate tab.