Maybe ... this all sounds very similar to my own experience, and thankfully I found the answer buried somewhere on this forum. Kicked myself when I realised:
In Black Shark options/controls, you have to select the Category dropdown for "Axis Commands". It's the 2nd one (after "All"), on mine it is even highlighted red text on a green background. :doh:
You cannot assign axes in any of the other categories. For example, the "Ins Cyclic Stick" category only allows you to assign buttons.
Hope this helps!