Sumproduct with 5 criteria

I've attached a zip file to hopefully make it easier to explain this.

On the variable tab you can see the from and to dates for each month (basically the start and end dates for each month)

On the DataEntry#2 tab you will see projects by rows (you can have the same project more then once - on multiple roles), with contract signed as a Y/N, the price (an hourly rate), and then the number of hours per week in columns S through AF.

What I need to do is sum up the total revenue per month (using the from/to dates) for each project (sum across the potentially multiple roles), and differentiate if the contract is signed or not.

The aggregated $ amount is posted on the DataEntry #1 tab (I have highlighted one such cell in Blue under the Backlog title - column AR). This would be all revenue in June for project 001 that has a contract signed (Backlog).

Your help would be greatly appreciated.

Jeff