I know exactly, what you mean Mike, as I have the same issue with another setup. I have 3 persons in the same room, attending a Zoom conference with 40 people around the world. These 3 persons are covered with 3 Sony RX0. I've also added an additional HDMI switch on the Input 4 with 2 more RX0 with a wide angel view of the room plus a MacBook Pro, which shows slides and clips.
The output of the second MacPro goes trough a HDMI distributor, which delivers the Zoom image to 3 monitors for the persons in the local room, so they can see all the connected Zoom attendees.
My task is, to use the Multiview output for my external director's monitor and stream to Zoom trough the USB-C connection on the ATEM Mini Pro. So I have no output free to record the clean program output
The only way to get a good signal is either to record all RX0 internal or - like I do it in my final setup - route all 6 RX0 trough 6 Blackmagicdesign bi-directional HDMI to SDI converters. So the HDMI loop trough of the converters feed the ATEM Mini Pro and the HDMI switch, while the SDI output of the converters goes into 2 Atomos Sumo to record the clean Signals. Means, that I have to re-edit the program output in the post.
Of course, it would also be possible to use the Sumos as a multi view device instead of the ATEM, and record the output of the ATEM at the free input of the second Sumo, but then I am missing the other features of the Multiview-output of the Mini Pro.
So it still would be great to have a possibility for recording and streaming on the USB-C output at the same time. After reading all these anwers here, the only left solutions in my opinion could be:
1. find a device, which makes it possible, to record the USB-C output stream of the ATEM and lets the same signal trough to the MacBook which is running Zoom, or
2. find a device, which can record the "stream ethernet output" (which kills the ability to connect the BM software via ethernet), or
3. record the multi view output and zoom in the program window (where it is not possible to remove the overlayed background of the insert - even if I delete the letters) at the postproduction, which will result in quality issues, or
4. record the Zoom conference on the MacBook via the integrated Zoom recording function, which also will be a great loss of quality.
Maybe someone here finds another solution. Please excuse my Austrian English