I think I would do something like this:

my $my_addr = 'my.box.ip.addr:80';
my $keep = 0;

while (<>) {
  if (/incoming connection/) {
    $keep = /\Q$my_addr/;
  }
  print if $keep;
}
[download]

That will go through the log and print out just the lines you're interested in. For each incoming connection, it will print all the lines up to the next incoming connection, only if the connection line contains your IP address.

(Hopefully, the ASCII data for one connection will end before a new connection starts, otherwise you're kinda outta luck...)