Auto-fill table values from source table with "rules" to handle multiple values?

I have a long table which is formatted properly to create a PivotTable. However, the data I need to display is text, not numerical values, so I cannot use a PivotTable.

I would like to use some Index/Match trickery to simulate a PivotTable with this data. Basically what I would like a formula which will:

1.) Match the row and column headings of THIS CELL to two columns in the source table, and enter the value from the source table's VALUE column
2.) If there is no value that matches, leave THIS CELL blank
3.) If there are multiple values that match, use the Source Table's "DATE" column to find the most recent value.

Attached is a simplified spreadsheet which should make it perfectly clear.

Thanks so much

(P.S. If there is a more efficient / elegant way to do it than INDEX/MATCH, I'm happy to hear it).