So Luma Locale Switcher doesn't affect at all? Meaning, if you changed the game to boot like it's from the US region, it wouldn't display in English? Because the system's language is in Jr regardless..?
I would suggest trying it if you haven't. In the case it didn't work, you have 2 options, either get the US version of the game (either digitally or a cart), or do a region change. There's no other way around that. If you have no progress with this jp cart, i would suggest doing the former.
If you find the Japanese language cumbersome to navigate through with and without the game, and you are willing to sacrifice eShop access, then do the region change.