Echo Speaks Is very powerful, but also fairly complex to set up.
You could do everything already described with Echo Speaks just with Alexa routines and a virtual device, but unfortunately, none of that gives you what you asked for, which was the ability to change the display on the echo show.
FAQ: Can I trigger an Echo Action without Speaking to It?
I may be mistaken, but I don’t think Amazon exposes that ability at this time.
For details on the installation process for echo speaks:
https://tonesto7.github.io/echo-speaks-docs/
You can ask any additional questions about echo speaks in the author thread for that code: