I hope I don't need to take apart my 3ds...
BAD NEWS: broh... you have to take it apart.
GOOD NEWS: You made a backup of sysNAND. I'm jealous.
INTERESTING NEWS: Since you're doing it anyways, might as well mod a micro USB port into the 3DS just in case it ever happens again.
MOST BOGUS RADICAL INFOMATIONAL NEWS DUDE: Yes, they have
tutorials on GBATemp on how to do this.
If you can mod an Xbox controller you can mod a 3DSXL. It's not that hard.
You will need all your regular soldering tools and a special screwdriver (I use the same one I fix iPhones with) some pcb parts, wire, and an SD adapter card (I have so many lying around I use them as tokens when playing magic)
Live in Jersey? Take a trip down to Rutgers and I'll help you... you can read some comics and homepass while the soldering smoke smells up the room. It's a great high.