KingPepe was kind enough to direct me to the existing dump, and so I'm going to temper my claim: Mine appears to be the first unmodified dump that's publicly available.
The other dump uses mapper 241, which nesdev describes as "dubious", but which is well-supported by emulators because it's trivial. My cart uses mapper 178, which is poorly supported by emulators. I'm fairly confident that I'm correct in the mapper, and if nothing else, the bank-switching code is the only difference in the actual PRG banks between mine and the other dump. So, either there were two releases of this game which used different mappers, or whoever made that dump modified it to be more compatible. Thus, I shall still claim victory