Help needed with IF and COUNTIFS Formulas

I believe the problem you are having is due to round off errors

as you can see the 8:30 AM in cell H5 is rounded up to ....7 while the 8:30 AM in cell AA3 is truncated at ....6

this error could go either way.  Forcing a ROUND(AA3,9) and of the values in columns C:P may be needed but rounding of columns C:P will cause propogation of roundoff error as they 'build' on each other.  and you can't use ROUND(H5:H15) in the COUNTIFS formula because that must be a range.

You could convert that whole formula to use something like:

=LET(t,ROUND(U3,9),s,($B$5:$B$15=$R$4)*
         ( (ROUND(--$C5:$C15,9)<=t)*(ROUND(--$D5:$D15,9)>t)
        -(ROUND(--$G5:$G15,9)<=t)*(ROUND(--$H5:$H15,9)>t)
        -(ROUND(--$K5:$K15,9)<=t)*(ROUND(--$L5:$L15,9)>t)
        -(ROUND(--$O5:$O15,9)<=t)*(ROUND(--$P5:$P15,9)>t) ),
        SUM(IF(ISERR(s),0,s) ) )

in this case I round all the values to 9 digits and then do the comparisons.  

I will edit this if I think of something better.