Another option that you have is to rely on professional software. It would obviously require some financial investment. However, if you are frequently working with PDF files it would be totally worth buying.
There are a lot of special software tools designed to fulfill the needs of translators, copywriters, and other people, who may need a professional PDF word count. For example, Anycount, which is one of the more popular choices allows you to easily recognize and count the text in PDF in many different languages. What is more, it follows a clear and fast word count process. Therefore, you would waste much less time counting the words. Finally, professional software is a reliable option, that a lot of professionals already use and had given feedback on. That means that you can carefully evaluate the software before using it.