I managed to fix the issue with my noise functions, and as such the fBm is producing much more terrestrial looking planets. I've also taken the improvements I've made and made it so that I can regenerate a planet using a different seed.
I was surprised to find my program actually running faster than it was doing. In addition I was expecting, when I regenerated the noise, for the program to stall momentarily. However it turned to be the opposite: It quite happily flies through generating them, as shown in the video.