The ignore_elt parameter doesn't do what you think it does. It tells XML::Twig to pretend that element doesn't even exist. So what you want is to remove that, and then inside the title function, check where you're at. One way is this:

my $twig = XML::Twig->new(
                          twig_handlers => { $sel => \&title},
                          pretty_print => 'indented'
                         );
# ...
sub title
{
    my ($twig, $tit) = @_;

    $tit->set_gi('tit') unless $tit->level('title') == 2;
}
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This means XML::Twig will read and parse the title/title/title elements, but when we get there, we check how many levels of title's there are above us, and if that is 2 (that means we're the 3rd), then we don't set_gi.

Good luck.