That's only 2 mm thicker than the XGC(without batteries holy christ). I would be astonished to see that completed, that is some serious pocket sized gamecube right there. It would be your legacy, so make sure to give it a memorable name.
To answer your question, just wire the 3DS stick straight up. X to X, Y to Y and so forth. Ghost movement is practically non-existant when playing normally. That said, I've got some chips and a programmer coming in the mail and I've been doing a little research; plans are to make the 3DS stick work with a stock 64 controller with zero ghost movement via adjustable deadzone. If all goes well, it shouldn't be too hard(probably easier if I get the deadzone code to work because I wouldn't need the conversion code) to tweak it to gamecube.
SS