People like to point out that they can't play 1MB ROMs on hardware, but it's not like something can't be made to support it. The MMC5 was specifically designed to handle ROM sizes up to 1MB.
The best bet is to start emailing etc those brilliant people who design flashcarts etc and let them know that there is a demand for such a product.
You speak as if it's really that simple. To date, there are no physical NES cartridges that support 512KB on PRG (legit or not), and no NES games ever required more than this. What incentive would there be for a flashcart designer to put effort into designing and attempting to sell a cart that may be usable for only a few games, to a very narrow audience?
And it's not just as simple as making a cartridge support more than 512KB on the PRG-ROM chip. Does the MMC5 mapping support a CHR-RAM and W-RAM configuration (this is specific to the FF3 pcb design; Source: http://bootgod.dyndns.org:7777/profile.php?id=1507
)? There can definitely be more challenges depending on the uniqueness of the original cartridge created to house a specific game.
I realize that not everybody cares about playing this game on the original hardware, but at least trying to create a product that can
be played on the original hardware gives weight to the authenticity and effort you put into your work. For this project specifically, it isn't just some balancing hack or remixed gameplay, it's much closer to the finished work of what Nintendo should have delivered to the U.S. and Europe, so that fans of the series could experience games like FF3 on it's intended console.