Following up to an earlier post...
There is a Little Frank label on the 4,1/5,1 motherboard next to a ‘diagnostic port’. Emailing across the pond, I’ve heard that this port might allow a pathway to easily flashing a modified MP51.0085.B00 image using the Bus Pirate.
More exciting.... The possibility of a plug-and-play firmware upgrade for NVMe that runs whilst plugged into the diagnostic port.
Regarding the SPI-chip, it was mentioned earlier by gilles that the chip model was SST25VF032B. According to the datasheat http://ww1.microchip.com/downloads/en/DeviceDoc/20005071B.pdf the chip uses 10mA at 2.7-3.6v. So the reason why a USB-powered port shouldn’t be enough would be phantom current draw by other components, maybe? And if you needed to power ALL 3.3v components on the board to get a stable 3.3v you would need more than a usb power supply could deliver I think. Because if you put 3.3v on the power-pins of the chip, every 3.3v component will get power, not only that chip. And maybe the large amount of components on the board draw more current. But to be sure you would need to measure it and verify it with a multimeter. Maybe the 3.3v is pulled down to 2.5v by all components because of the current draw.
So maybe the diagnostic port thing is the best bet? Good find by the way!