I'm sorry dear, but according to documents the
TWL(DSi) titles(Games) only stored on NAND(inside 3ds).
The productor that produce that NAND chip is Toshiba, and that is a customed 1GB flash.
You have several ways to try:
1.
telephone your nintendo support, tell them about that problem. (But that only makes low possibility since ninty doesn't want people to dive into their hardware - especially those related to their motherboard. but you can try it.)
2.
Help the HACKERS in 3dbrew by donate a few to the decapping fundraiser. (The reason why i think this is more likely to be succeed is, when they decapped and analysed the chip, we can make many use of that. oh, well that may take not a time long..) you can even tell them the problem you're facing in the email
you send to them later.
If successfully decapped they can even write new firmwares to let you use SD to store those games, thanks to their efforts. (but
no CFW or firmware now, sorry)
3. Buy a FPGA or other board, use
your talent to remove that chip from your 3ds's motherboard softly, and use softwares to test the pinouts. if the result is not the similiar with other NAND chips, forget it and donate and softly put that back onto your 3ds's board. if the result is similiar,

you're lucky -- go buy one with
bigger size and same working condition (so you would have to test if trying this method) and try put the new one onto your 3ds's board, then post one about how to do so on Gbatemp (Someone will try to document that). hope your 3ds get no damage when you doing these things.
Reminder:
That is not an easy job to remove and stick the chips on motherboard (
easily damaged).
Conclusion: If you're newbie to hacking, Let the experts try solving your problem.(so help decapping is better choice)
So..well. Hope you a good day.