I have a similar setup at home with an M5Paper[1] to display a daily screenshot of my homeassistant dashboard. It's a neat little device based on an ESP32 chip with an e-ink display and some sensors.

I never thought about using a Kindle, even though I have an old jailbroken Paperwhite... It fits so much better for this usage, and would certainly have saved me days of working around hardware limitation.

[1]: https://shop.m5stack.com/products/m5paper-esp32-development-...