OR conditions in a SUMPRODUCT formula

I am using SUMPRODUCT to build a stats page for a report. I need a lot of different combos of the data and SUMPRODUCT usually works like a charm for me. But I'm stuck. In this particular case I have two columns, each containing multiple values. I want to pull data for a subset of values from each of those columns (using "<>" multiple times will be just as onerous).

I'd like to try to keep it simple.... and had hoped that something like this would work. But this returns an error.
=SUMPRODUCT((Severity={"BI","NI","XY"})*(Type<>"Duplicate")*(Time<5)*(Source={"A1","A6","A7","A12"}))

I can get it to work with this option but this means that my formulas will become very long.
=SUMPRODUCT((Severity="BI")*(Type<>"Duplicate")*(Time<5)*(Source={"A1","A6","A7","A12"}))+SUMPRODUCT((Severity="NI")*(Type<>"Duplicate")*(Time<5)*(Source={"A1","A6","A7","A12"}))+SUMPRODUCT((Severity="XY")*(Type<>"Duplicate")*(Time<5)*(Source={"A1","A6","A7","A12"}))

I tried using an OR condition for the Severity but that gave me the wrong value. I played around a bit thinking it might need to be treated as an array formula, but that was a disaster. I feel like I'm missing something simple.... or that I really will have to build long formulas.

Any ideas or suggestions?