You can route an audio stream into any channel of any audio device so even if the controller shows 9 channels, you can use all of them if you provide enough sources.
I've added 8 (*2, stereo) channels to OBS at some point for shit and giggles and that worked fine without interrupting my normal headphones. Things can only work better without the compatibility layer.
Your biggest issue trying to get this done will probably be picking the right channels for the right controllers because you have no idea what controllers are what on other systems. An audio device dropdown after some auto detection should work, but if the controller has weird specialised channels that don't follow the normal system output (i.e. 5.1 but two channels are actually stereo headphones and not real 5.1) then configuration may be a pain.
I didn't play around with it much, but the controller did appear as a 5.1 (or was it 7.1?) in Linux.
Oh, and I forgot, the controller itself also has a headphone jack. The controller itself can take 3 audio streams, two of which can be used for sound.