You might want to update the OP, there's a way to extract a private header with Powersaves which is a far cheaper option than buying a GW and/or a low-FIRM 3DS.
https://gbatemp.net/threads/tutorial-get-your-private-header-using-powersaves.385511/
https://gbatemp.net/threads/tutorial-get-your-private-header-using-powersaves.385511/