garygid:
Is there usable, non-volatile memory in the RTC?
Since the RTC is reset with each power-On or Reset, it is mostly
useless, so if it has real EEPROM, that could be used?
The RTC does not have any EEPROM, it has RAM which retains state while VDDBU is powered (as does the RTC unit). On the Due VDDBU is connected to 3V3. Even if you found a way to power the RTC via a battery, it looks like it only has two words you could use for user storage.
Really the best thing is to have a genuine external serial EEPROM, it's a pity the Due does not have one. They are quite small and cheap, perhaps Due v2 will have one.
It would be possible to hack one in by wiring to the SPI header and gluing the EEPROM on top of the SAM3X8E, just needs a SOIC8 breakout board.