What you propose is called tunnelling (tunneling (US spelling) is preferred in some places although I am unsure if it is a technical term a la colorimetry (universal spelling) or not) and as you mention it was tried a few times but some were fake and others abandoned.
Three ways out of it as far as I see and none that you will be able to pull off with what you appear to know right now:
(external) hardware level repeating. Not especially complex (it is only 2Mbit after all) but costly and distance. I would probably look at modding a DS to do such a thing (similar to the early homebrew local play with 3 DS or something like the demos).
Hacking in wifi to the game, not such a bad idea as many games use a standardised fairly low level format from what I have seen (especially with the download play stuff: see the download station hacking for a loosely related example). It would be hundreds of times more complex than any hack that has presently been (seriously) attempted.
Emulator based. Essentially being what you want it may be possible to rig up something similar to VBAlink real (a long defunct fork of VBA that allowed you to play link games with a real GBA and your PC, now missing a lot of information such as the lead schematics from what I recall). This is similar to the tunnelling you mentioned although emulation rather than encapsulation presents a whole host of interesting technical questions and challenges. This is also hampered by a lack of gaming grade emulators for the DS (plenty of development and hacking grade ones but playing is a different matter).