Making a save compatible with a console other than the one from which it originated

[AMCL]

Hello! I'm hoping someone here can help me with a problem I have, since I've been through official channels, escalating until I got to someone with no authority to escalate further, and Nintendo claims there's nothing their repair team can do.

In the course of trying to move my Pokémon data (X and αS) from one SD card to another, I suspected the new card had been corrupted and formatted it. The problem is that I formatted it using the DS, which also formats the DS without warning you that doing so will change the DS's identifier to the effect that it treats its own data as if it had come from another console and refuses to read it.

It seems to me that there must be, somewhere in the data (which is itself perfectly fine), a reference to the original identifier. Presumably, it's also possible to manipulate the data to change this reference to the new identifier or to manipulate the DS to change the identifier back to the old one (I imagine the former is easier).

I thought a hacking community would have some experience with this kind of thing, so I thought this would be a good place to ask. I'm prepared to do any hard work involved myself, but I'd have no idea where to start without being directed. These saves represent hundreds of hours of my time, a nearly complete Pokédex, and contain Pokémon I caught in Gen IV that I've had for seven years. I'm completely determined to get them back. Starting again isn't an option; nor is giving up.

[Kaphotics]

Reformatted sd card === new sd card => new crypto keys for save decryption. If your backups are not already decrypted you are out of luck.

[AMCL]

I have the original microSD, which isn't reformatted; it's the same as it was when the save was created. I also have a new, blank, bigger microSD that's never had anything on it. The internal memory in the DS is reformatted. Is that a problem?

[Kaphotics]

If the console cannot read data from the old sd card, it's obvious the console nand was updated to decrypt the new sd card and won't work with the old.

Since the saves are completely lost, it may be best to invest in homebrew so that you can recreate your favorites, and have backups for the future.

[AMCL]

Is the required key hypothetically anywhere anymore? Is that information lost irretrievably - not for practical purposes, but absolutely?

[gnmmarechal]

Is the required key hypothetically anywhere anymore? Is that information lost irretrievably - not for practical purposes, but absolutely?

It is lost. Pretty sure of that.

Sent from my cave of despair where I collect souls

[AMCL]

There goes my plan to take over Nintendo/the world. Now I'll just have to invent time travel, I suppose...