Advanced SUMIF - date range including missing dates

Hello,

I need to sum a range of cells by the date in the corresponding column headings - only the dates in the column headings may or may not be continuous.

So eg. for the week starting 12th Oct, I need to sum where the headings is >= 12Oct and <19Oct, and the start/end date may/may not be available, because the system wouldn't return anything if there hasn't been any sales for all the products on a certain day.

Dummy cells are welcomed if needed, I can easily blank them out as white text in the final output.

Attached below is a sample file that illustrates what I need, a formula for the yellow cells. At the moment I have manually sum them up but ideally I want to replace it with a lookup formula that I can copy-and-paste across to the right.

Advanced sumif.xlsx

Any help would be greatly appreciated, thank you very much in advance!