Well if they locked the ROM inside the chip, then you can't do anything.
But if you are lucky and it's writeable you could look at the cart updates from Ace3DS+, they produced the same hardware found inside the blue cart and they released updates which write to the internal ROM once, so maybe editing it gets you somewhere.
Another possibility would be to try flashing it with a hardware programmer. I didn't look further into it, but iirc there are pins above the mSD slot (SPI?) which are probably used during production to flash the internal ROM ... maybe you can get something from there.
Last possibility is to just buy another flashcart for 5$
Updating the bootstrap is a lot more painful than spending a few bucks on a cart which works on the latest 3DS., or even 15$+ on a cart which gets bootstrap updates pretty quick after Nintendo pushes another 3DS FW update (like DSTWO).
Regards,
iCEQB