So, the method suggested by ramses seems to work.
Here are the basic steps.
The goal is to have a DAW mix of sources connected to the Babyface Pro sent to a DAW for effects, combined with DAW midi instruments or backing tracks, and all sent to Zoom. To keep things simple, this example has just one mic connected to the first XLR input of the Babyface Pro, and one MIDI track in the DAW.
A. In TotalMix:
1. Click on the AN 1/2 output (bottom row).
2. Enable Loopback for the AN 1/2 output.
3. Raise the fader for the AN 1/2 output.
4. With the AN 1/2 output still selected, raise the fader for the software input AN 1/2 (middle row).
5. Note: DO NOT raise the fader for any other physical or software input.
B. If you want to monitor with headphones, in TotalMix:
1. Click on the PH 3/4 output (bottom row).
2. Raise the fader for the PH 3/4 output.
3. With the PH 3/4 output still selected, raise the fader for the software input AN 1/2 (middle row).
4. No Loopback is needed here.
C. In TotalMix:
1. Click an unused output in the bottom row. Let’s assume you pick ADAT 8. (If you see “ADAT 7/8” rather than “ADAT 8”, you should make “ADAT 7/8” mono and then ADAT 8 will be shown separately).
2. Enable Loopback for the ADAT 8 output.
3. Raise the fader for the ADAT 8 output.
4. With the ADAT 8 output still selected, raise the fader for the AN 1 input (top row) (that is, where the mic is physically connected).
D. In the DAW, set the main output to channels 1/2 if not already set. For example, in Ableton that means setting "Master" to channels 1/2.
E. In the DAW:
1. Set the MIDI track to the main DAW output (e.g., "Master" in Ableton).
2. Turn on monitoring for the track (for example, in Ableton select "In").
F. In the DAW:
1. Create an audio track.
2. Set the audio track’s input to the channel corresponding to the output chosen in step (C). For example, if the output chosen was ADAT 8, and the DAW is Ableton, this would be channel 12.
3. Set the audio track's output to the main DAW output (In Ableton, that's "Master").
4. Set the new track to software monitoring (in Ableton, that's the "In" setting).
G. In Zoom’s audio preferences:
1. Select the Babyface as the “microphone”.
2. Select the Babyface as the “speaker”. This will allow the audio from others in the Zoom meeting to go into your headphones. I saw a YouTube video stating that this may cause a feedback loop for the other people, but I tried it out briefly and did not experience it, yet.
3. Uncheck the “Automatically adjust microphone volume” box.
4. Check the “Show in meeting option to Enable Original Sound” box under “Music and Professional Audio”, and check all the other boxes here unless you have a reason not to.
5. When you start the Zoom meeting, use the option to enable original sound at the top left of the screen.
As noted above, I tested this setup briefly today and it seemed to work.
If you have another source connected to the Babyface, like a guitar on the INS 3 input, you'll need to replicate steps (C) and (F) for that source, using a separate unused TotalMix output and a separate DAW audio track.
Hope all this helps and works!