Wouldn't "spicy pillow" be the main problem with old iPads? My iPad Air 4th gen doesn't have an option to limit charging to 80% etc.
My old iPad lasts weeks on its battery if I don't use it, I can only imagine it actually sleeps and would not answer network requests in this state.
Congrats for the successes :-)
Air 3 I've got on ebay-like site holds pretty well but the same model that my partner got from official dealer had always issues with touch recognition.