It occurred to me on the walk to work this morning that the sort problem can be fixed by introducing a sort key:

# @data as used previously
my %sums;
my $sortKey;

for my $datum (map {[++$sortKey, "$_->[0],$_->[1]", @$_]} @data) {
    if (exists $sums{$datum->[1]}) {
        $sums{$datum->[1]}[4] += $datum->[4];
        $sums{$datum->[1]}[5] += $datum->[5];
    } else {
        $sums{$datum->[1]} = $datum;
    }
}
   
my @result = map {[@{$_}[2 .. 5]]} sort {$a->[0] cmp $b->[0]} values %
+sums;

Dump (\@result);
[download]

Output is as shown previously - the dates are all in the same month.