A big shout out to Pizza Pasta (The New New Era) for a very helpful tip on getting Earthbound Zero to run on the nesDS. I'm quoting his comment verbatim:
You might know this by now but Earthbound Zero is totally playable in NESDS, you just have to mess with it a little on your computer.
All you have to do is open Earthbound Zero in a NES emulator on your computer (I used Nestopia) and get to a point where you can save a file. After you save, transfer the Earthbound Zero SAV file into your NESDS roms folder and you should be able to resume your game in NESDS. Hope this helps.
Yups, it helps! Thanks man. And yeah, portable Mother/Earthbound Zero FTW!!