Based on your SUMIF you should find the below works:

=SUMPRODUCT(--(tblExeTimes!$B$2:$B$6000>=B1),--(tblExeTimes!$B$2:$B$6000<C1),--(tblExeTimes!$G$2:$G$6000="Nathan"),tblExeTimes!$F$2:$F$6000)