there IS a simple solution. You'll have to open the DVD drive, and replace the laser with an identical one. you can replace the entire "sled" assembly. but the DVD logic board MUST stay with the xbox's motherboard. (unless you have away to flash the board)
you'd need an exact match for that port. And someone with a good bit of soldering experience. Flux, a desoldering gun for the anchor points. It should be possible - I'd find an experienced TV repair tech.
I've seen a couple of 3DS systems with this issue. My solution was no to fix the socket, but to charge via the "contact points" on the back - rather than using the actual power socket. (look for a dock for your system) the contact points seem to run to a different part of the system than the power socket. if that doesn't work either - I'd try to find something similar to nyko's Charge Base for the original 3ds (it has it's own charging system - separate from the 3ds)