You really cant, But you can use Save Data Filer yo backup all your saves then follow my tutorial and just reinstall and reimport all your saves. This happens because the "code" for when your logged in with a linked NNID is still in your EmuNAND. The only way would be to follow my Tutorial. When this error happens you "Want" to lose data so that you can relink an NNID and properly login.Really glad to know this method is confirmed for O3DS people, I've been confused a lot by how to do this without issue.
But those steps mean you have to use savedatafiler? Anyway to just...not use that at all? I found this topic while searching for a way to keep all data working on the emunand (created before formatting sysnand) but with no issue logging into NNID.