Thanks for the link to Epson support! I reached out them and they referred me to this link:
How to Safely Remove USB OTG from Android - Technology Hint
which turned out to have the answer (it's an android OTG question, not a Movario question, but Epson support was gracious and non-judgmental).
There are two issues remaining, however:
1) You can't actually run a movie directly from the USB device. Instead, you must copy the file you want to view onto the
Moverio device's storage before using it. Pretty much not what I wanted. It might be an OTG thing, I don't know, but I'll check with Epson support to see if I'm missing something and will report it back here. If anyone has experience with this, please let me know.
2) The
Moverio "Lost" the connection to the device at least once...where I couldn't unmount it and couldn't see any files on the disk. I turned the Movario off, disconnected the USB, turned the
Moverio back on and reconnected the device and all was well again: (View, copy, watch, unmount). That worked, but I hate inconsistent behavior in devices.