From LiveHTTPHeaders, I get that I need to do this:

GET https://somesite.com/foo/bar;jsessionid=0001CxASgCKob1dDFdsSDSDF:-
+1?requestor=AGE&doctype=Statement&docid=NTczMyT1LTc5LTMtMS0wLQ%3D%3D&
+token=df99a322563f
[download]

So I coded it up like so:

    $url = URI->new("https://somesite.com/foo/bar;jsessionid=$jsession
+Id");
    $url->query_form( 
        requestor => 'AGE',
        doctype => 'Statement',
        docid => $docid,
        token => $token,
    ); 
 
    $response = $agent->get($url);
[download]

But I get "400 Bad Request".

The above code is the last step of a five stage process where I log in, navigate, collect cookies and headers and whatnot to fill in the variables.

I have verified that all the previous steps work great with nice return codes and the HTML content is just as it should be, matching what I get with a browser.

Since you can't really test your answers, wild guesses are OK in this thread :)

UPDATE:
Amazing Fact: The HTML error page that is returned with my 400 actually contains a URL. The error page says that the URL is no good, but if I paste it into a web browser location line, it works and pulls the pdf file down.