I red the whole thread now and I can't believe there is still no Plugin from hCaptcha for BF; since this is requested about one Year ago.
Maybe a look at Viktor Vogels Easy Cal Check (ECC - free version) can help you get an Idea for the Code. --> kubik-rubik.de/ecc-easycalccheck-plus
I would love to see a release of this Option very soon.
thank you for your sharing one of a possible solution for this integration, I hope that this question will be as soon as possible done, we'll inform you about the progress this theme.
Thanks all for your patience!