I'm trying to do the same thing. For now, I'm trying to input the HDMI output into another systems capture device to use as a Zoom camera/mic. Ultimately, I'd like to send the signal to some Teradek gear, as well. I tried the projector program output. Haven't completely troubleshot it yet, but so far it seems OBS doesn't recognize the connected device as a "projector" option to select. I'm using a 2013 imac with thunderbolt to HDMI connection to PC laptop with HDMI to USB 3.0 capture device.