Here's what I would do.

First, get a list of all of the hash keys you want to sort. Since the hash is so deeply nested, it may be easiest to store the results in an array ref:

foreach my $k1 (keys %bighash) {
  foreach my $k2 (keys %{$bighash{$k1}}) {
    ...
       push(@keys,[$k1, $k2, ...]);
[download]

Now that you have the keys in an array, you can sort them:

@keys = sort by_key_total @keys;

sub by_key_total
{
  $bighash{$a->[1]}{$a->[2]}{$a->[3]}{$a->[4]}[$a->[5]][$a->[6]]
     <=>
  $bighash{$b->[1]}{$b->[2]}{$b->[3]}{$b->[4]}[$b->[5]][$b->[6]]
}
[download]