Thank you so much! I took the Live HTTP Headers from Firefox and compared them with what I was sending with:

my $filled_out_request = $forms[1]->click;            
print $filled_out_request->as_string;
[download]

I found what I was sending was correct. The trick was a) making the actual request with UserAgent (which 'click' alone does not do) and making sure cookies were setup properly.

Hats off to Corion!