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There's a way around that requirement by the way. If you take the game apart and remove the battery the Data will clear from the SRAM after about 2-3 seconds, I suggest replacing the battery with a socket and not screwing the cartridge back together. That way you can rinse and repeat until you get one you want, also RNG is the same at every boot sequence so if you start too quick you'll get the same results.

Works better than the long term quest and only requires going through the start sequence and tutorial so it's technically shorter than the quest, downside though is you'll have to play the game again.

If you have a Cart dumper you can try your hand at Hex editing the SRAM data to get one you want but be warned this method has a lot of bugs and can lock you out of achievements if done incorrectly, if you're already late in the game it also comes with the drawback of permanently soft-locking if you for whatever reason attempt the quest, since the game autosaves at the beginning of the quest.

Note: if you play the Remastered versions it's easier since those you can just format the memory card, or on modern consoles and PC just delete data manually, you'll need Homebrew to edit the saves on newer consoles, still easier than the cartridge, and it still does softlock at the quest, though you can avoid it on the 6th gen consoles by pulling the memory card before autosave. On PC save editing is extra easy and there's even a tool that can do it, which also prevents the softlock if you want to go on the quest later. There's also a mod on the PC version that get this, allows multiple genders (way more than just two) right from the start and you get to pick it manually and not randomly, I know, wild isn't it. PC really is the master platform.