Hi Pagoda-100, I have no experience with Blackmagic, I use an Atomos Ninja V to record my audio and visuals. I am very happy with that solution. It works very easy and it records 4K ProRes 60fps easily.
It records the audio/visuals on its own ssd drive that is hot-swappable, so it is very easy to copy the recordings onto my Macbook. I inserted the Ninja V between my MacBook Pro and my screen, so I can record at any time. I just switch the screen resolution (to full HD usually) and change the sound output in Ableton Live and I am ready to go. This is an example of a video recorded this way: https://www.youtube.com/watch?v=qtbSHYHKDmI