A family of Microsoft spreadsheet software with tools for analyzing, charting, and communicating data.
I feel sorry that I don' get your real purpose at first.
My solution is similar to your second formula, remove some unnecessary part. "" won't affect the result of sumif.
I suggest you calculate separately then add together.
SUM G=SUMIFS($G$2:$G$10,$B$2:$B$10,$C$15,$C$2:$C$10,$D$13,$D$2:$D$10,$D$14)
SUM F=SUMIFS($F$2:$F$10,$B$2:$B$10,$C$15,$C$2:$C$10,$D$13,$D$2:$D$10,$D$14)
SUM E=SUMIFS($E$2:$E$10,$B$2:$B$10,$C$15,$C$2:$C$10,$D$13,$D$2:$D$10,$D$14)
Then result =SUM(I2,J2,K2)