What BIOS update method did you try? If it wasn't the Recovery method, please try that. Instructions are at Intel NUC Boards and Kits - BIOS Recovery Update Instructions.
I've forwarded this on to our BIOS engineers and they are investigating. Apparently, the newer BIOS version 0028 included an update to the Management Engine, which is likely causing this error. Oddly though, version 0028 was posted to Download Center on November 7 and this is the only report about such an error.
For now, I'd recommend you use the Recovery update method to downgrade back to version 0023.
I have about the same problem. When I load the 0034 image straight from the Intel downloads it works fine. When I load it with ITK, do nothing, just save it in ITK, it wont flash. I get the same 1566 error.
I have checked the files but they are byte identical. The only thing that is not identical is the creation date. Is that a part of the CRC check?