I wonder when or if there is a right or responsible time to advertise installing beta software onto a live site. What do you think?

There isn't. Naive clients should never be encouraged to try beta software just because and that goes 10x for something that takes over and drastically alters the core reason for WordPress' existence, creating and managing content.

This is actually the hardest part of this and why I think Gutenberg should live as a plugin for longer - it changes something so central to site operation that it's unlike almost any other feature rollout. Training will be needed, possibly theme updates, etc. At the same time, we absolutely should want Gutenberg used in a wide variety of installs.

That tension ("test widely vs make sure you aren't breaking existing content process") will likely slow any wide rollout. I'd never deploy this on a live site for a client until it was feature complete, stable, worked with things like ACF that I have widely deployed and I could spend some time with the client to walk them through the different workflow.