Success! Thanks for the advice, everyone.
Here is the story for those in a similar situation:
I have a CycloDS Evolution + EZFlash 3-in-1 for my DS Lite.
Don’t bother downloading GBA EXPloader or anything, CycloDS can handle all of the GBA emulation on it’s own. What happened to me was exactly what was described here:
“Your problem sounds like a case of mistaken identity. Is the Jap. version of Mother 3 the most recent game you played in your 3-in-1? If so, use GBAExploader to erase the NOR memory in your 3-in-1, then load the translation with the CycloDS. That should work.”
I guess I had tried to run the Japanese version of the game a long time ago, and so that was stuck in my 3-in-1. I put a different GBA game on it, through EXPloader, to over-write the old Mother 3 (because I couldn’t just find a way to erase it). Then, I erased EXPloader and put a freshly patched Mother 3 back on the CycloDS. From there, I just ran it through the CycloDS’s normal menu like I would any game and it did the rest of the work (erasing the other GBA game, and putting the new Mother 3 on).