Does the datasheet say you can do software can change the BOD? I don't think it does.
28.2 Fuse Bits
The ATmega48A/PA/88A/PA/168A/PA/328/P has three Fuse bytes. Table 28-4 - Table 28-9 on page 283
describe briefly the functionality of all the fuses and how they are mapped into the Fuse bytes. Note that the
fuses are read as logical zero, “0”, if they are programmed.
This includes the Extended fuse byte for BOD.
28.2.1 Latching of Fuses
The fuse values are latched when the device enters programming mode and changes of the fuse values will
have no effect until the part leaves Programming mode. This does not apply to the EESAVE Fuse which will
take effect once it is programmed. The fuses are also latched on Power-up in Normal mode.
28.8 Serial Downloading
Both the Flash and EEPROM memory arrays can be programmed using the serial SPI bus while RESET is
pulled to GND. The serial interface consists of pins SCK, MOSI (input) and MISO (output). After RESET is set
low, the Programming Enable instruction needs to be executed first before program/erase operations can be
executed. NOTE, in Table 28-17 on page 295, the pin mapping for SPI programming is listed. Not all parts use
the SPI pins dedicated for the internal SPI interface.
So, I read it as something the software can't do. An external programmer is needed. Need to check the references in the prior post as well.