OK! You have some problems with the underlying logic.
IF( AND(H7 > G7, F7 > E7), "Late", six_more-IFs(check_down) )
If that very first AND delivers TRUE, then it doesn't even go on to check the remainer of the IFs. That carries through with the nesting: Once row 9 returns a TRUE in the third nested IF, it won't even check rows 10 - 13 because those are in the ELSE term that is not checked because it already returned a TRUE.
Anyway,
If you just want to know whether the MOST RECENT ITEM is "On Schedule" or "Late",
then:
C6 =INDEX(C7:C13, MAX(MATCH(1000000000,H7:H13,1), MATCH(1000000000,F7:F13,1)))
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