I only skimmed through this, but for that first foreach, you should have something %seen in place just before entering the loop, so it takes id/sequence as a key to skip alternates in the loop (next if %seen{$sequence}.)

Also, I'm probably wrong, but the way you describe your process sounds like a gather/take from Perl6. Here's some Perl5-ish implementation using Syntax::Keyword::Gather:

use Syntax::Keyword::Gather;

my @sequences = ( ... );
my @filters   = ( ... );

my @primary_and_filtered = gather {
    my %seen;
    for my $seq (@sequences) {
        take $seq unless $seen{$seq};
        take map { $_->($seq) } @filters;
        $seen{$seq}++;
    }
};
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Note that the @filters doesn't correspond to your described filters list of sequences, but rather, a list of filter functions (e.g. another permute, or a more specific search, etc.) to evaluate your original primary sequence against.