I think I figured out a workaround: it's possible to "sort of" do this using the NDI Output Plugin (
obs-ndi - NewTek NDI™ integration into OBS Studio).
You can set the NDI Output to be the Program Output (so this would be all the audio channels going to whatever livestream you're doing), then open NDI Video Monitor for the output on the same computer (or different on the same network). Set OBS to have the "Audio Monitor" go to one audio device with whatever channels you want going there, and NDI Video Monitor play audio (the same as your stream) to a different device.
Another option: you can add "Dedicated NDI Output (Audio Only)" filters to each audio source. The only problem being you can't assign multiple audio sources to have the same "NDI Name" and work at the same time. You could (I guess) have multiple NDI Video Monitors up and mix after that.
Latency on the same computer isn't terrible (maybe <200ms).
Alternatively, you could use the
Multiple RTMP outputs plugin, and run a local RTMP server on the same computer to pull audio from, but I'm guessing audio latency might become an issue.