Actually, if you buy a Power save device (IE, the cheating device of the 3DS), you can actually back up your whole save file and later restore it using it and your computer.
It's not JUST for cheating, and many people actually bought one simply for this purpose.
They're 15 bucks on Ebay and it might be worth the investment if you're that interested. There's really no other way past buying a new cart.