Hey Michael, what do you think of building an HDMI-to-UVC device? Basically a device integrated in a cable with 2 ends: HDMI and USB. It would capture the video output of a computer, emulate a USB video class (webcam) device so the USB end can be plugged into another computer which would be able to see the video output of the other computer using any standard webcam software.
Heck it could even be powered by the USB host. It would be an "active cable" that doesn't require any custom software. Would be super convenient to carry with a laptop for data center technicians.