Also, the readme says to change 0x6 with a hex editor, but... What/where is 0x6? I did open the rom with HexEdit but don't know where to go!
The NES rom header is the first 10 bytes in the rom. It's essentially metadata and tells the emulator what kind of cartridge it is. In this case, for around 20 years, all roms identified the game as having a battery backup, which is patently false. This patch is based on the latest no-intro set which has a correct header. So I doubt you'll find the latest dump on rom sites, which usually have outdated dumps. Aware of this, I offered a way to correct the dump in the readme. So 0x6 is offset 0x000006. In other words, the 6th byte in the entire rom, as illustrated in this picture, which is a rom dump you'll usually find online.

Change that circled
52 byte to
50. That change should fix it, however, there's some dumps with some extra metadata afterwards, so make sure the entire 10 byte header is...
4E 45 53 1A 20 40 50 00 00 00 00 00 00 00 00 00
Does that make sense?
All roms I get are with WRONG checksum (I used the online patcher provided in the link) — however, the game gets translated and runs fine, at least first screens.
Forcing the patch with a bad checksum should be fine, honestly. The only difference between new and old dumps is the header, so data isn't being shifted around which would throw things off.