If you are "hard coding" the criteria values into the formula you could avoid TRANSPOSE by just using ; separators in the second array constant, i.e.
=SUM(SUMIFS('Data Table'!S$7:S$200,'Data Table'!$D$7:$D$200,{3050,3100,3150,3250,3300,3350,3360,3400},'Data Table'!$C$7:$C$200,{52510;52518;52519},'Data Table'!$A$7:$A$200,"FNE"))
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