Summarizing data by row and column headers

I am looking for a single in-sheet non-VBA formula solution to summarize values by row and column labels.

I am familiar with SUMIFs but this formula does not appear to be able to handle this use case. I can solve this with the likes of HSTACK but that still involves setting up multiple formulas manually within the master HSTACK formula. I am more interested in a formula in which I define the array, column headers, and row headers, and it summarizes appropriately. INDEX and MATCH comes close, in a sense, but it is limited to returning the first matching result rather than summarizing all matching results.

I am using Office 365 desktop. My knowledge is intermediate.

Here is some example data. I will not be working with large data sets.

Original Data

And here is the result I'm looking for (I would provide the row and column headers - the formula would only be expected to return the summarized data into the array)

Desired Result