Sumif formula with duplicate rows and columns

Hi all,

I have a potential sumif problem. I'd like to be able to sumif based on 1 criterion for a row and 1 criterion for a column, except the criterions duplicate across the rows and columns. The exact names of the rows will not be equal to the columns and vice versa, but the rows can duplicate names among themselves, and same with columns.

I'd like this formula to be able to drag and drop in the highlighted portion of my exact attachment.

Is this a feasible formula? I gave a sizably truncated example but imagine another 500 rows and columns.