Do you have two SD cards that are 4 GB or larger? There's a way to use your o3DS NAND image on your o2DS through EmuNAND. This is not something typically done because it constitutes as an unauthorized System Transfer. This can get both your 2DS and 3DS banned if the 2DS connects online with the 3DS profile. You would have to keep your 2DS turned off at all times and delete the EmuNAND afterwards.
This method is very involved, but it would check if your:
I) 2DS motherboard's internal NAND is failing (an extremely rare occurrence).
II) 2DS SysNAND firmware is incorrectly flashed
III) neither NAND nor firmware is at fault (other, unknown hardware failure assumption)
Would you be willing to try this? I need to let you know that it requires exact steps to follow, may not fix the softlocks, and that the procedure is highly controversial under normal circumstances.