Average range with multiple columns and rows with multiple criteria

Hi Everyone,

Need some help please. I need to gain an average from a range that spans multiple rows and columns based on criteria that is within different rows and columns.

I have tried the below formula but now appreciate AVERAGEIFS cant handle this requirement without some further integrated formula?
=AVERAGEIFS($F$6:$CH$15,$F$5:$CH$5,">="&$B$7,$F$5:$CH$5,"<"&$B$11,$E$6:$E$15,$B$15)

Attached is a sample sheet