My question is: is there anything I could have told Perl to give it a hint about how to perform the match...?

I'm wondering if a divide-and-conquer approach might give you the same effect, while being clearer to Perl about how to match without needing to backtrack.

  while ( $mmap =~ /^(.*\n)/mg ) {
    my $line = $1;
    print $line if $line =~ /$pat/;
  }
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