INDEX IF Syntax: Minimum Value In J13:U13, And Displaying The Value For The J1:U1 Accordingly

=IF(B13=9.9999,"",INDEX(J$1:U$1,1,MATCH(MIN(IF(Summary!$F$3:$Q$3=TRUE,$J13:$U13,FALSE)),J13:U13,0)))

In the formula above, it's basically looking for the minimum value in J13:U13, and displaying the value for the J1:U1 accordingly. The "MIN(IF" portion of the formula, tells it to exclude certain columns based on true/false statements on another sheet. The whole thing is working properly, with one exception:

For example, let's say that K13 and N13 contain the same value, and that value is the MIN value in that range. Also, I have disabled the K column on the Summary sheet. Despite the fact that the "MIN(IF" is properly disregarding the value in K13, (which i know it is because this works properly when there are no duplicate values) the INDEX portion of the formula isn't looking for the true/false values on the Summary sheet, and displaying the value in K1 instead of N1 simply because K comes first.

Is there a way that I can tell the INDEX portion to also look at the true/false statements on the other sheet, or can I have it recognize what actual cell the "MIN(IF" portion is selecting and return the correct value based on that?