Figured it out.
Long story short: The Tracktor Audio 2 mk2 IS a 4-channel soundcard and works with the iPhone & iPad as such. What I missed is that channels 1&2 are treated as the main stereo channels and controlled by the iPad’s hardware volume. All you need to do is raise the iPad volume to the max (say with the volume buttons) and possibly reduce it to the level you want with the Main setting within dJay. Now both the Main and Pre-Cue outputs of the Audio 2 work as expected.
One more thing: if you experience the device dropping on and off, it is because it is drawing too much power from the iPad USB-C input. To resolve this either use it via a powered USB hub or get the external power supply for the Traktor Audio 2 mk2.
This is what clued me in:
