Necessity breeds innovation, so I've hunted around for an alternative, and turns out what I've found might be better.
The latest Quadstick firmware (2357) allows a PS4 controller to be plugged into the back of the Quadstick and to pass its input through to the console/PC. Extending this idea, an Xbox Adaptive Controller can be plugged into the same port, using the Brook Wingman XE converter to make it look like a PS4 controller to the Quadstick. This setup looks like this:
XAC - - - - - - - Brook Wingmwan XE - - - - - - Quadstick - - - - - - - Console/PC
You need to have an appropriate config file on the Quadstick that allows it to see and pass the PS4 controls through, such as this one:
And here is a profile I built for Apex Legends: