Not a Perl solution, but if all else fails, you could try pdftk's flatten option (worked fine for me so far)

$ pdftk filled-form-doc.pdf output flat-doc.pdf flatten
[download]

___

[flatten]
       Use this option to merge an input PDF's interactive
       form fields (and their data) with the PDF's pages.
       Only one input PDF may be given.  Sometimes used
       with the fill_form operation.
[download]