Instead of using a webserver, have your Perl script fork off its own server (if one isn't running at the time). It can communicate on a socket. We have a CGI program that keeps an large XSLT in standby. Using IO::Socket:

my $sock = new IO::Socket::INET ( LocalHost => $server,
                                  LocalPort => 9200,
                                  Proto     => 'tcp',
                                  Listen    => 2,
                                  ReuseAddr => 1,
                                );
die "socket creation error: $!" unless $sock;

while( my $client = $sock->accept() ) {
  binmode $client, ":utf8";
  $client->autoflush(1);

  # Read data
  while( $client->recv( $in_buffer, $buffer_size ) ) {
    # Store data
  }

  # Process data

  # Return data
  $client->send( $output );
}
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Some things to consider to make it dummy proof is allow it to adjust what port is runs on at runtime, and to have the server exit after a while to avoid zombie processes.