If you don't mind me asking, what kind of mods will you be doing on your New 3DS? Some kind of video-out mod for streaming?
I don't mind at all! Just sending it out to be modded so that it will have a video-out for streaming, exactly as you said. It'll be a while before it happens - I prefer one of the two modders who are offering the service, and the one I prefer is still designing the board. Usually part of the case is cut to allow for access to the video-out, so modding a limited edition New 3DS XL would almost feel like treason.
Sounds cool. Do your preferred modders happen to have websites for their services? It's not something I'd have done any time soon, but it's an interesting idea for something to do down the road. I'm assuming that the video output goes to your PC, yes? It sounds cool to be able to output 3DS games to a TV from a PC. 
I don't think I'd want to have a limited edition New 3DS modded either, especially with how much harder they are to get a hold of lately with all the scalpers and whatnot.
Yup, the two modders you'll usually see named off when people talk about 3DS modding is Loopy (3dscapture.com) and Katsukity (3dsvideocapture.com). They're often mistaken for each other (as you can tell by the URLs), but the big thing is that folks usually care about is that Loopy is US-based while Katsukity is Japan-based, and Katsukity offers a lot more in regard to what systems they will mod. Loopy currently only does DS and 3DS (non-XL, non-New) but is currently working on the XL boards and the New 3DS XL. He also just put up the mod (for self-install only) for people to plug in various controllers into their 2DS/3DS/3DS XL.
You should expect to pay about $200-$250 for the installation of a capture card into your 3DS, though he hasn't put any prices up yet. I have a DS modded from him, and that only cost $75. No telling if the regular 3DS capture card will also go down in price.
The video output goes to your PC, so you can play 3DS/DS games on your computer monitor. It works great for my modded DS! The original DS's screen is pretty terrible compared to a 24" computer monitor, ha.
