Pending a reply from RGBlink (who asked me a few questions and have now gone very quiet) I have continued experimenting and tweaking.
I've been able to livestream successfully using the RGBlink Mini as a single source into OBS and then out thru YouTube. It proved the concept, as the RGBxxx did exactly what it was supposed to with three HDMI sources connected. However, the video was extremely jerky and freezing all the time on both the stream and the OBS recording. I'll give it another go in a while, dropping the sampling rate somewhat. I'm somewhat surprised as it's a reasonably powerful PC... and it handles the RGB thru Zoom with nary a glitch...
As Mark One says, this live-streaming aspect needs lots of working through...
Mark: A friend in a church in Oxford that does live-streaming now has a minimum of three people for each stream: one for sound, one on the ATEM and one handling production/cueing people etc.