I upgraded from an original 3DS to the New 3DS when the new one launched and my system transfer went smoothly... except for one problem which I didn't discover until today. For some reason, my NNID wasn't registering when I tried to do anything online-related (such as the eShop) and so I couldn't update Smash and redeem my Mewtwo code. When I called Tech Support (which was very friendly and helpful, by the way), she said I would need to format my system and re-connect my NNID to the 3DS. "Okay," I thought, "this should be easy enough." Well, I did and that went smoothly enough, but now I have a whole new problem that I didn't stop to consider because of my haste to claim my prize: ALL MY ACHIEVEMENTS, MII PLAZA PUZZLE PIECES, STREETPASS MIIS AND EVERYTHING ELSE I BUILT UP IN MY SYSTEM OVER THE PAST 4 YEARS IS NOW GONE. Yes, I understand that's what formatting the system would do, but I was upset over my Smash/Mewtwo/NNID woes and didn't think things through. I never claimed to be the brightest Poké Ball in the pile.
Now, here's my question (finally): When I transferred my system data from my original 3DS to the New one, I did so physically using the widely-recommended SD card transfer method on my computer. When I did this, the tutorial I used recommended that I make a copy of the folder that held all my 3DS information and leave it on my computer in case something happened, so I did. (I hope that's legal, it didn't seem like it wouldn't be and it's not like I'm using it maliciously or unscrupulously) Now, if I were to, say, go through the agonizing process of opening my New 3DS again, popping out the SD card and copying that backup data back onto it, will I get back what I lost? I'm only really concerned about the stuff I lost in my Mii Plaza, such as my Puzzle Pieces, Find Mii/Find Mii 2 progress, hats and my 1000+ StreetPasses, since my games can be re-downloaded (though I'm betting the save data for those games is gone for good. Oh well, another excuse to play them again, I guess.) I know it sounds silly, but I was really rather proud of all that. Or would that not be part of what got saved?
Something else I just realized: Would recovering all that (if it is indeed possible) delete the one thing I did all this for in the first place, my beloved free Mewtwo download? I know I'd be able to buy it again later this month, but tomorrow's my birthday and I kind of considered Mewtwo a birthday present from Nintendo itself and I'd hate to lose it like that, only to PAY for it later, especially given all the trouble I went through to earn it in the first place. I know, that's very silly of me, but it's the principle of the thing. That seems like a poor reward for my loyalty to Nintendo for all these years, even if the mistake is totally on me at this point.
Can my Mii Plaza data (as well as anything else from my system) be recovered? And if so, will it cost me my early Mewtwo? Please help! D: