Is it possible to login to a secure web site via JavaScript with Perl?

As a subscriber to The New Yorker, I have access to their archive of all back issues. In order to access them I click a Login button, which evokes a JaveScript (javascript:RVViewers[0].subscription.doShowLoginPanel ?) which display a new window to accept my username/passsword.

I had hoped that by logging in via Safari on my Macbook Pro, I could 'piggy-back' that session in a Perl script to download all pages of given issue:

# Logout 'on click' button
# href="javascript:RVViewers[0].subscription.DoLogout(false)"

# Login 'on click' button
# href="javascript:RVViewers[0].subscription.doShowLoginPanel()"

use LWP::UserAgent;   
for($page = 1; $page < 200; $page++) 
   {
   $number = sprintf("%07d", $page);
   $url = "https://archives.newyorker.com/rvimageserver/Conde%20Nast/N
+ew%20Yorker/1948_02_07/page$number.jpg";  
   $ua  = LWP::UserAgent->new;
   $req = HTTP::Request->new(GET => $url);
#  In Safari address box - javascript:prompt('your%20agent%20string%20
+is',navigator.userAgent)
   $ua->agent('Mozilla/5.0 (Macintosh; Intel Mac OS X 10_14_4) AppleWe
+bKit/605.1.15 (KHTML, like Gecko) Version/12.1 Safari/605.1.15');
   $ua->credentials('archives.newyorker.com:80','web_server_usage_repo
+rts','user' => 'password');
   $res = $ua->request($req);
   if ($res->is_success)
     {
        $number = sprintf("%03d", $page);
        open IMAGES, ">///Users/wmfs/New Yorker (1948-02-07)/Page $num
+ber.jpg" or die; 
        $result =  $res->content;
        print IMAGES $result;
        print $number . "   okay\n";        
     } 
   else  
     { 
        print $url . "\n";
        print $number . "\n";
        print $res->status_line . "\n";
        die;
     }
    }
[download]

Unfortunately, after the first two pages (which appear to be available even without a subscription), I face the dreaded "403 Forbidden" message.

Any help would be very welcome.

Thank you, Bill Seabrook