Thanks for the replies so far. In my case, I'm using RT::Client (not sure if it's on CPAN - I think $work paid Best Practical to write it). It uses a custom LWP UserAgent class so it (hopefully) should be straightforward to add a header on outgoing requests. Now I just need to dive into LWP to figure out how to set headers.
my $rv = $self->SUPER::new(%args);
$rv->ua( LWP::UserAgent::RTClient->new($rv) );
$rv->ua->{keep_alive} = 1;
$rv->ua->{requests_redirectable} = [ qw( GET HEAD OPTIONS ) ];
Thanks,
Drew