Align S-type column headers

I’m very unhappy with the alignment of the headers in the following table. I’ve even tried using multicolumn, but it has no effect. (And if someone knows what the table is about… Yes, I’m unhappy with the content also, LoL!)

documentclass{article}
usepackage{siunitx}
usepackage{rotating}
sisetup{round-mode=figures, round-precision=3, scientific-notation=false}
begin{sidewaystable}
    centering
    begin{tabular}{rrr@{}S[scientific-notation=true]@{}S[scientific-notation=true]rSS}
        toprule
        $N$ & $P$ & $P^3$ & multicolumn{1}{c}{$Delta x$} & {$Delta t$} & $n_t$ & {w.c.t. (si{minute})} & {Speed-up si{percent}}\
        midrule
        16 & 1 & 1 & 0.393 & 0.196078431 & 102 & 4.069515 &  \
        32 & 2 & 8 & 0.196 & 0.0980392157 & 204 & 8.13903 & 1 \
        48 & 3 & 27 & 0.131 & 0.0653594771 & 306 & 13.1286 & 0.929919793428088 \
        64 & 4 & 64 & 0.0982 & 0.0490196078 & 408 & 28.5765 & 0.569630990499186 \
        80 & 5 & 125 & 0.0785 & 0.0392156863 & 510 & 48.5749 & 0.418890723398298 \
        96 & 6 & 216 & 0.0654 & 0.0326797386 & 612 & 87.7083 & 0.278389730504411 \
        112 & 7 & 343 & 0.0561 & 0.0280112045 & 714 & 96.3564 & 0.295637912997995 \
        128 & 8 & 512 & 0.0491 & 0.0245398773 & 815 & 197.87 & 0.164532875120028 \
        midrule
        32 & 1 & 1 & 0.196 & 0.0980392157 & 204 & 55.5835 &  \
        64 & 2 & 8 & 0.0982 & 0.0490196078 & 408 & 111.167 & 1 \
        96 & 3 & 27 & 0.0654 & 0.0326797386 & 612 & 197.713 & 0.843396741741818 \
        128 & 4 & 64 & 0.0491 & 0.0245398773 & 815 & 415.779 & 0.534740811825513 \
        160 & 5 & 125 & 0.0393 & 0.0196270854 & 1019 & 1076.27 & 0.258222843710221 \
        192 & 6 & 216 & 0.0327 & 0.0163532298 & 1223 & 1867.37831666667 & 0.178593162951207 \
        224 & 7 & 343 & 0.0280 & 0.0140154170 & 1427 & 2435.0328 & 0.159786143332443 \
        256 & 8 & 512 & 0.0245 & 0.0122699387 & 1630 & 3343.32016666667 & 0.133001919598786 \
        bottomrule
    end{tabular}
end{sidewaystable}

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