No problem, and I wish you luck!
Tried to look into a flashcart based solution, but can't find much of anything that'd help - if you want to look into that more, look into an "autoboot" function on a flashcart. I may just be missing something.
Oh! One more thing, excuse me for the double post, but it seems sellers on Etsy sell reproduction DS cartridges. You could buy one off there if they sell the game you're looking for, or perhaps ask if they could make you one? The ones they make may not work unless you have custom firmware on 3DS, though.