When I started thinking about this cheap encoder project, I assumed it was more likely than not that it wouldn't be good enough for household TV watching. To hedge my bets, I ordered a standalone HDMI encoder box. It's this one:

I selected this one according to the Cheap and Lazy algorithm. I saw it mentioned by some other people, and it was inexpensive relative to others mentioned. It was also readily available with just a short delay. The day I bought it, there was also an instant coupon for US$20 off the price.

I ran the same sort of POC test with this device that I ran with the cheap encoder dongle earlier. Results were pretty good. Here is what vlc says about the stream:

vlc was able to consume and display a very clear image with both H.264 and H.265 codecs. Despite best efforts, I was only able to get a frame rate of 30fps. I'm not sure if that's a limitation of the device, a limitation of the Fire TV stick, or some other settings thing. The video and audio were completely smooth in vlc.

As a side note, there was some small inconvenience as a side effect of buying the least expensive device. The setup instructions are for Windows (whatever that is), and the device comes configured with a static IP address of 192.168.1.120. I already have a device with that address, so I had to temporarily turn it off while I configured this new device. Luckily, there is a simple web UI that lets you change the network configuration and various other things. There was an unexpected bonus (because I didn't pay attention to it while shopping). The device can record to an SD card for subsequent download. I don't know if I'll ever use that, but it's nice to have.

Regardless of what happens with this overall project, I should be able to scratch my single-channel itch with this device after applying some software magic.