Hi Spencer! I went through the exact same headache with my old e-reader a few months ago. It had been reliable for years and but suddenly it refused to connect to Wi-Fi, even after I restarted it, forgot the network and re-added it, and updated the software via USB. My phone and other devices connected without issues, so I knew it was the e-reader itself, and being in a small space, signal wasn't the problem.
What finally worked for me was just biting the bullet and replacing it with a newer model. I got the Amaz, and it connected to my Wi-Fi right away without any fuss. The improved hardware in this newest version, with its faster performance overall, seems to handle connections much more reliably, and the longer battery life means I don't have to worry about it dying mid-download.
You do not need some fancy app stack to win this. Pick one number, like 45 minutes after homework, and celebrate the handoff with a goofy family timer song. Make it the same every day and keep charging cords out of bedrooms. It feels simple and everyone gets it fast.