... it'll give me full control over the order since I can include any LIST not just sorted keys.

But still basically operating on values...

sub base_code  {
   my ($h_codes) = @_;
   for my $h_planet ( @$h_codes{ sort keys %$h_codes }) {
      for my $a_aa ( @$h_planet{ sort keys %$h_planet}) { 
         for my $codon ( @$a_aa ) {
            print $codon, "\n";
         }
      }
   }
}
[download]

or for convenience

sub sorted_values {
   my $h_ref =shift;
   return  @$h_ref{ sort keys %$h_ref }
}

sub base_code2  {
   my ($h_codes) = @_;
   for my $h_planet ( sorted_values $h_codes ) {
      for my $a_aa ( sorted_values $h_planet ) { 
         for my $codon ( @$a_aa ) {
            print $codon, "\n";
         }
      }
   }
}
[download]