(Re-)installing CIAs will over-write your game saves.
How many games do you have? There might be a way to recover those saves, but this method is very tedious, and it may or may not work.
- Let's say you had the game Pokemon Omega Ruby (EUR) installed on your original 3DS setup.
- You have your old setup backed up on your SSD like you mentioned.
- You already tried copying and pasting that entire setup onto your reformatted SD card but nothing shows up, including Pokemon.
- What you want to do is make a new setup with none of your old files.
- Next, you install a fresh copy of Pokemon OR with the Title ID of 000400000011C400.
- Once that game is installed, you look in your backed up setup. Your Pokemon game is located at:
- You'll see two subfolders, content and data. Your encrypted save file is located in data, named as 00000001.sav .
- Copy and paste over your old *.sav to the one found on your new setup / SD card.
- Try launching Pokemon Omega Ruby and check if your save is restored. If it is great.
- If your save doesn't work, the game might have anti-cheat detection. Recopy the save file and try using either Checkpoint and/or JKSM to see if they detect your old save.
- Should the old save gets identified, try backing up that save. Doing this will make a decrypted copy of your save file.
- After backing up your save, try restoring it back to Pokemon.
- Check the game again to see if your save was successfully restored.
Edit - IF you need help identifying games to Title ID, use :
Edit 2 - You should do a single example in your inventory first to see if this works or not. If it does work, there's a way to automate grabbing copies of only your saves using a program Duplicate Cleaner Pro by Digital Volcano Software (you figure out how to obtain this).
For LOTS of games
1) Install all your games with matching Title IDs on the new setup.
2) Use Duplicate Cleaner Pro to search for all files named as 00000001.sav found in the old setup.
Be careful not to delete anything, or make another copy for safety sandbox.
3) Copy or extract those saves. This program has the ability to maintain folder directories.
4) Paste those saves to overwrite the ones found on your new setup.
5) Use Checkpoint and/or JKSM to make decrypted back ups of your saves.
6) Restore them all; do this to eliminate guesswork of which games have anti-cheat detection.