Spent an hour with Amazon customer support. No resolution, but at least I think they are more informed about the issue. We did a screen share session so they were able to see the problem for themselves. If you are having a problem with a recent Fire, I definitely recommend initiating the call on the device itself and then requesting a screen share.
I now have Fire OS 5.3.1.1. We downloaded the .bin directly using Silk, moved it to storage folder, and executed the update, all without USB cable. But it didn't update the Kindle app.
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