This one comes with an honest limit worth reading before you start: it converts the WORDS, not the design. You get editable text in a file Word opens, which is what you want when you need to rewrite a document — and not what you want if you need the layout preserved.
Free on every plan, including the free account. Prices in AUD.
Pick it from the convert section of the tool list and drop your PDF in. It opens immediately, with nothing uploaded anywhere.
The text is pulled out of the PDF and written into a Word-compatible .rtf file. Word, Pages and Google Docs all open .rtf without anything extra installed.
Open the downloaded file and rewrite it as ordinary editable text. The words are real text, not a picture of text, so you can search and change them.