Maybe I'm misunderstanding something, but why not simply put the processing in the loop?  (together with some condition that detects when a 'packet' is complete)

Something like this:

while (defined(my $line = <$NA_Conn>)) {
  $input.=$line;
  if ($input =~ / ... /) {
    process($input);
    $input = '';
  }
}
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