A simple fix which might help a bit is to grep the array before running sort on it:

for (sort {
        $a->{RegionNum} <=> $b->{RegionNum}
        or
        $a->{AR}        <=> $b->{AR}
    } grep $_->{RegionNum} == $RegionNum, @StatsArray) {

    $ARKey = $_->{AR};
    # do stuff, no need to check the RegionKey.
}
[download]

Untested.