Is the NUC otherwise stable? I.e. you don't have RAM issues or something? Check the SHA1 sum of the .BIO it should be:
As a last resort you could try the recovery flash using the jumper. But before you do that you can try another method yopu have not listed: Press the power button on startup for a little longer than usual and release. There should pop up a recovery menu from which you can flash.
The NUC has been stable, no RAM issues, and the sha1 checksum matched the one you posted.
So I started thinking perhaps it's the usb drives (both USB2) that I've been using, let's try an USB3 stick.
To my surprise that one didn't show up at all in the F7 menu, so I restarted to try the F7 from within Visual Bios.
It showed each and every partition on my system, but still not the USB3 drive. Then, still in the F7 file browser, I browsed to the copy of the SY0036.BIO file in my Downloads folder on the hard drive and loaded it. The NUC restarted and applied the update in about 3 minutes!
Still don't know what went wrong with the other USB drives, might be that the NUC is picky about them.
Anyway, loading the SY0036.BIO file from local hard drive works a charm for me.