Sum column exclude duplicates

I've got data for different regions of our company. For this example, what I need to do is count the number of jobs in the "South Atlantic" region (Column T) that are NOT "Wal-Mart Stores, Inc" jobs. In order to do this, I put a "1" in Column F so that the formula would have something to sum:

=SUMPRODUCT(--(T2:T1079="SOUTH ATLANTIC"),--(H2:H1079<>"WAL-MART STORES, INC"),(F2:F1079))

The problem is that some job numbers, which are located in Column G, are duplicated. As a result, this number is higher than it should be.

So what I need to do is only count each job number once. How do I do that? Is there a way to modify the existing formula? Or do I need something completely different?