The SAM has IAP (In Application Programming) instructions that allow an application to write into flash.
I see no reason that a library could not be written to emulate EEPROM storage, or indeed re-task the current EEPROM API.
AFAIK nobody has done this yet but I'd say it would be high on the priorities list.
If I had full control over the SAM3X, that would not a problem due that you can use the sectors that already exist in the internal flash memory and manage it as a good file system.. but the Arduino IDE does not give me that capabilities, (Or my ignorance about this tool hides me the capabilities of it) instead, it erases the whole flash every time you program it.
I was thinking in tailoring an external EEPROM, maybe adding a FRAM board like this one:
(FM24CLXX FRAM Board FM24CL16 Memory Storage Module Development Board Kit 3.3V)
The access is via I2C, for another 16K of non-volatile memory...