I've been reading up on AVRs myself; I'm not the most knowledgeable, but this is what I've picked up in my research.
First, I realize you are disabling your BOD to save power, but this is listed as a preventative method to avoid EEPROM corruption in the ATmega328P. From section 8.4.2:
Keep the AVR RESET active (low) during periods of insufficient power
supply voltage. This can be done by enabling the internal Brown-out
If you are really keen on disabling the BOD, it is possible to have it disabled when in sleep mode. To accomplish this, you can set the BODS bit in the MCUCR register.
Like you, I have become frustrated with the ambiguity in the voltage which at which the AVR's EEPROM will become corrupted. I see nothing in the datasheet. However quoting Atmel's EEPROM Corruption article on their website:
a regular write sequence to the EEPROM requires a minimum
voltage to operate correctly
Minimum voltage? This is a generic article, so I'd guess this refers to the lowest voltage at which the ATmega328P operates at, which is 1.8V.
Hope I've helped.