I would assume that's how it knows what's installed on your 3DS.
What happens if you just copy the .sav from your SD card? Back them up to your computer, reinstall the .cia and then paste them back?
And next time, use rxTools to backup your title.db
Won't work. You see, the issue is that I deleted title.db in preparation for pasta, and then I realized that I didn't need to do that. (And i couldn't retrieve it with recuva either.) Since I had no access to eShop due to a linking issue, I just formatted the thing. Since saves are encrypted, they won't work on my new id after the format.
I really don't want to resign to lose my Persona Q map data or my Senran Kagura Burst save data, so I'm trying anything that could potentially work.
EDIT: I did it! I restored my old NAND, emuNANDed it and was successfuly able to update to 9.8, and I was also pleasantly surprised to see that NNID linking isn't really tied to the IDs on the Nintendo 3DS folder, just the serial number of the 3DS. From there I just replaced files on my PC and was able to restore my old saves.
Thanks to all who responded!