I guess I'm still out of luck. I got a replacement PW3 for my wife because the battery wouldn't hold a charge. It has version 5.8.10 on it even after a reset. I tried updating with the version indicated in post 1 and update is greyed out. I then tried downloading and updating with 5.8.7.0.1 but the kindle says I've got an invalid update file.
So, "no soup for me!"
I'm updating with a Mac on 10.12.6 (Sierra).