SumIfs / Sumproduct for table with vertical and horizontal lookup criteria (text+dates)

Hi,

I've tried searching other threads and post for similar problem and applied various solutions without any luck.

I have 2 sheets within a document, 1 sheet (data_inputs) contains a table of data across a calendar year by weeks.
On the 2nd sheet (monthly) I want to summarise specific values by month.

I've tried a hybrid of sumifs and stumble across sumproduct but can't get my sheet to work.

The monthly table needs to calculate the number of 'things' that were completed & recorded each week within the given monthly period.
The labels along the horizontal fields represent the text lookup values. As the weekly period starts and finishes from Saturday to Friday, I've added in a reference row on the data_inputs tab to reflect what monthly reporting period the values need to be added into on the monthly sheet. I've also add in the 1st and end of each month to try set the range.

See attached document for reference.

Any help is appreciated.

Thanks
Ben