Mechanize doesn't meet my needs in this case (as far as I can tell). LWPcook was exactly what I needed -- see PROXIES.

The following got me logged in to the website programatically, which then allowed me to open the links in the site ($links) to view their content($body).

$ua = LWP::UserAgent->new;
$ua->proxy(['http', 'ftp'] => 'http://user:pass@proxy.site');
            
$req = HTTP::Request->new('GET',"$link");
            
$res = $ua->request($req);
            
$body = $res->content;
[download]

It is important to make sure that proxy.site is not the url that you entered in the tools options of the web browser as the proxy server, but is the one that comes up on the user/pass request box when you are entering those values manually when requested (that took me a while to figure out).

Thanks for pointing LWPcook out. There are a number of copies out there, but the only one complete one is on CPAN at http://search.cpan.org/~gaas/libwww-perl-5.808/lwpcook.pod