This is not going to be trivial. That you're already asking this question already indicates that it's going to be a long journey. I'd rather use a barebones and to-the-point file upload component of another component library such as Tomahawk's <t:inputFileUpload>. It only doesn't support asynchronous uploading and you need to make the submit button of the form a non-ajax one, but it does the job you want it to do without much hassle.
You can find in this answer detailed step-by-step instructions how to integrate and use it in your project: JSF 2.0 File upload. In case of PrimeFaces, you only need to make sure that you have removed PrimeFaces' own file upload filter from the web.xml, otherwise it would consume the uploaded file before Tomahawk's own filter get the chance.