You might have good luck reaching out to companies that produce reproduction carts. They'll often flash modded ROMs. I have a physical cartridge for FF6: Brave New World myself.
Look at an everdrive. I'm not sure about compatibility. I have a very old NES everdrive and some hacked games work while some don't. I would ask on the support forums for someone to try it out for you before buying.
I'm guessing it's going to depend on whether or not the original cart had any expansion chips? E.g. I don't see mention of the SuperFX chip that Starfox requires.
EDIT: I'm serious