I use checkpoint for my save backups. In fact, I ruined my own emummc while figuring out what your problem was in this thread. Checkpoint can backup everything at once (iirc) and can also restore everything later, or you can cherry-pick what to restore.
What I did on the emummc that I messed up, is mount it under the USB tools in nyx, then mount on my PC with HacDiskMount. I used that to save the entire user/save folder out of the nand. Actually, A detailed instruction and the tool can be found here:
https://gbatemp.net/attachments/libhac-with-saveextractscript-v2-zip.164018/
BUT... the folder naming is different from what checkpoint uses, so I had to start a game until a save was created, then back it up with checkpoint, then replace everything inside of that folder with the contents of the folder(s) created with that attachment. (hope I didn't lose you with that explanation)
Booting from sx to hekate/ams, you're better off powering down and using a dongle. Hekate/ams to sxos, you can simply reboot (in nyx settings make sure it replaces reboot to payload with hekate), and launch sx through the nyx payload launcher, OR there is a Payload Launcher you can use from HBL:
https://github.com/suchmememanyskill/Payload_Launcher/releases
In case you don't know where the payload is, I can't link it here but it's the "sx loader 1.0" on their download page. Seems the forums are down or taken out, but the download page is still there.