Hey you know what? I did go ahead and look more closely at the headers after your post and I had been using a non-URL-decoded value for a parameter called ctl00_ContentPlaceHolder1_ctl00_rcbusertype_ClientState. The encoded value was %7B%22logEntries%22%3A%5B%5D%2C%22value%22%3A%22Subscriber%22%2C%22text%22%3A%22Subscriber%22%2C%22enabled%22%3Atrue%7D and I used http://meyerweb.com/eric/tools/dencoder/ to decode it so now the following works:

$mech->set_fields(
            'ctl00$ContentPlaceHolder1$ctl00$rcbusertype_Input' => "Su
+bscriber",
            'ctl00$ContentPlaceHolder1$ctl00$txtUserName'    => $un,
            'ctl00$ContentPlaceHolder1$ctl00$txtPassword'    => $pw,
            ctl00_ContentPlaceHolder1_ctl00_rcbusertype_ClientState =>
            '{"logEntries":[],"value":"Subscriber","text":"Subscriber"
+,"enabled":true}'
);

my $response = $mech->click_button(
                            name => 'ctl00$ContentPlaceHolder1$ctl00$L
+oginButton',
                            x=>26,
                            y=>10
);
[download]

!