That you for the incredibly detailed and helpful review. Based partly on your blogging about your initial purchase, I pursued a similar end for our house, albeit with a “dumb” screen projector rather than a “smart” one (https://ruk.ca/content/yesterday).
I did, however, run into similar issues: plugging my laptop into the projector via a VGA cable I found that I was unable to stream Netflix to the projector because, somehow, the Netflix knew that I was streaming via a method that didn’t mitigate copying. Ultimately I found the “best” solution was to plug my Apple TV into the projector via an HDMI cable, which allows everything to work.
Our projector is small, but not as small as yours, and it is not battery operated, so it’s a little more difficult to find a good position for in the room, especially because its “keystone” control is not very helpful if the projector is at an angle: there is a control, but because it simply tilts something analog inside the projector, it renders ½ of the screen out of focus.
My jury is out on whether I can replace my TV with the projector, but certainly for popcorn movie nights I will go to the effort of setting it up.