Starting to work on USB port access. It appears the USB port has a Silicon Labs CP2102 USB-UART convertor. Drivers are available on this website:
http://www.silabs.com/products/mcu/pages/usbtouartbridgevcpdrivers.aspx.
Under MacOS X, this driver does install and presents a serial communications port as /dev/SLAB_USBtoUART.
The serial port settings appear to be 115200 baud, 8 bit word, no parity, 1 stop bit.
Watching this port shows output indicating the device periodically starts into a boot loader, an number of tests, ending in 'All tests done! BE Cube started'.
Pressing the factory reset while powered on produces the message "Config saved!" then goes through the same sequence.
This cube has now started presenting the configuration page periodically, whenever it doesn't show that it is running the self test via messages on the serial port. It is unclear if this was due to yet another factory reset with a prolonged depression of reset button, or solely due to waiting until the 'BE Cube started' message appears on the serial terminal and then accessing its web page. Once on the page, reconfiguration to another ip address was possible.
During mining the serial port outputs a sequence of a,b,c,d letters, in a mixture of upper and lower case.
When the cube cannot reach its mining pools, it appears to periodically reset, and during self test cannot be reached on the LAN port.
Therefore, if a cube appears unreachable, checking its serial port is useful as one can wait until it says 'BE Cube started' and then try and reach the configuration page.