I've not checked multi-channel embedded audio from a Blackmagic card, but with the Magewell Pro Capture cards (and NDI inputs) you can control the mix of the (eight) incoming channels via the Channel Mixer tab of the audio settings for that input. Each incoming channel can be routed to L, R or both, with a level control.
This does mean you have to commit to pre-mixing down to stereo and can't route individual input channels to different output groups (M, A, B), which would open up some interesting possibilities, but that's something which maybe should be a feature request (along with other ways of making use of multi-channel embedded audio feeds)?