Possibly related: one of the classrooms where I teach, on campus, has a fancy Crestron setup, and I had some issues like this. Campus IT added some "disable HDCP" button to the configuration panel and then everything worked.

In my dream of dreams, the computer would provide some feedback about what's happening rather than just flaking. I mean, I could go dig through Console logs, but something user friendly wouldn't hurt.

Dual monitor stuff: I think that's right for the original batch of M1 devices, having some limits on external monitors. I hope, but haven't tested, that everything works better with newer generation machines.