Then your best bet is getting a better internet connection
A N3DS with capture card now that they don't make those anymore is gonna cost you 700+$ while it's pretty much impossible to find a capture card by itself and only other choice is requesting a special unit pre-installed with a capture card from Nintendo Japan (since they have some meant for news outlets and whatnot). Also, based on your speed, unless you are also doing other stuff, you got more than enough bandwidth for at least 40FPS, possibly 57-60FPS if you get a better connection.