The built-in Mac compression methods were still not working properly, so as a test, I downloaded this mod,
I imported the mod, and it was accepted by PokéMMO without any issues. I then uncompressed then recompressed the mod to create a zip file that should be exactly identical to its source. After deleting the original mod from my mods folder and importing the new one, the same error appeared, confirming my suspicion that my Mac is not using the right compression method for creating mods.
It appears that there aren't very many compression applications for Mac, and all the software I can find result in the same error. Is there anything else I can do?