You ask about a "256KB EEPROM", but do you mean 256Kb? (Like the 24LC256?) If so, there is no way that would be big enough to hold all of the data. It only holds 32,767 Bytes. For your task, you will need...
7days * 8hrs * 60min * 60sec * 20Bytes = 4,032,000Bytes (about 32Mbit)
There are some serial (I2C and SPI) flash devices that I think are that big. (Microchip SST25VF032B)
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