Well 8 years later here is how to fix it.
Root cause: System ID of the Mii is different from current System's ID
1. Create any mii on the system you want to make him editable on (thats how we get current system's ID)
2. Run
JKSM, you may need the 06/30/2016 version, navigate to Shared ExtData --> F000000B --> Export Data and name it something you will recognize (like todays date)
3. Grab the
CFL_DB.dat file off of the SD card, either via ftpd or via moving it to your computer and grab the file you backed up from /JKSV/Shared/F000000B/<whatever you named the export>
4. Open the file with Mii Edit Tool
https://www.gamebrew.org/wiki/3DS_Mii_Edit_Tool
6. Also open CFL_DB.dat in a hex editing program, for example HxD
https://mh-nexus.de/en/hxd/
7. On Personal Mii tab look at system ID, press CTRL + F then select "Hex Values" tab, and type in the first few values of the system ID. It should be somewhere on the first or second line.
8. Go to All Miis tab in Mii Edit Tool and select the mii you created earlier, note the system id there. You need to change the values you found in hex editor to those valies, then CTRL + S to save.
9. Reopen the CFL_DB.dat in Mii Edit Tool and verify that Personal mii System ID matches system ID of the mii you created earlier. If it does, save the file again, move it back to the SD card and reimport via JKSM.
Thats it.