For MHX, check in "ExtData" for 00001554.
Monster Hunter X saves its games all on the Extra Data, no matter if you have a cartridge, .3ds or a .cia. It will always be in ExtData. Check there and export it.
This is a special case though, Capcom wanted to do something with powersavers but its just as easy to cheat now with homebrew.
Normally speaking though, .cia files save under "user" in SaveDataFiler.
.3ds files will save on .sav format on your 3DS' SD Card (NOT the Gateway Red SD Card).
Cartridge files will still save on the cart itself.
Yes i think this would preserve your savefile, but you can just use SDF/svdt and export it (check ExtData tab for MHX file), then back it up independently. I imagine backing the EmuNAND itself up would take a little longer than just the file