15.0.1 update didn't work OTA or through Finder.
Using
Apple Configurator 2, however,
did. No need to put into DFU or Recovery Mode, nor was it necessary to reset any settings or turn off WiFi.
The iPad did have to go through a data recovery (the screen "Attempting data recovery" came up, along with a progress bar), but that only took about 15 minutes for me and was successful. I left the iPad plugged in and had Apple Configurator still up during this time. As with any update, make sure you have a backup (either local or iCloud) just in case.
Something is obviously broken, but hopefully this helps someone.