To be honest, I don't think you can POST a PDF form. Generally PDF forms are just for easy printing or e-mailing. They're not intended to be a part of interactive web sites.
My only advice is to instead use the best tool for the job. If you want a web form, use a web form. That means HTML. In the end, you have nothing to gain by sticking with PDF; the only disadvantage is that you have to do a little more footwork to begin with. You could always try to convert the PDF
to an HTML form.