1st: I didn't use H2testw, but I will as soon as I can.If you used a different program other than [ H2testw / F3 / F3X ], those are not suitable for testing the hardware condition of flash storage. For example, the Window's built-in chkdsk (right mouse click on SD card letter drive → Properties → Error Checking) will scan and correct a SD card's file system but does not tell you if the card is fake or faulty.
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About the { CTRNAND + TWLN + TWLP }, there is a method of troubleshooting or repairing another person's 3DS firmware by temporarily cloning the (source) system's NAND onto another (target) system of the same [ old | new ] series. None of this would matter if your SD card happens to be bad where it can't reliably hold and transfer data.
2nd: So should I send you or someone else my System data?