The only fillable PDFs I've ever run into were PDFs that could only be filled in by users with the entire Adobe Acrobat Suite, so that program would allow typing in it and that program would be the one who saved the file.
Maybe someone else has better options, but as a Linux user who's never shelled out for Adobe software, I've never been able to fill in a PDF. Instead I print them out and write on them in pen. :/
But once you have a saved file, it sounds like you could have a webform with a file upload button. <input type="file"...> and have the form enctype able to handle PDFs.
If the whole thing's a webform, then maybe you there's a program to "read" the PDF and create a webform that is similar. I've not had any luck with programs like pdftotext since the PDFs I was dealing with were poorly created and the resulting text would be about 8 lines with thousands of characters each, and when pages contained two columns of text the columns ran together to form nonsense sentences. But a well-created, tagged and well-saved PDF shouldn't have these issues.