On the main menu, there is a button in the bottom right called "System Settings". This allows you to remap the keys used for menu input on both controller and keyboard. Notably, it has Up, Down, Left, and Right remaps which do not normally show up in the ingame button remap feature. These remaps will actually also apply to movement ingame, the game just doesn't inform you that this is the case.

So to summarize, to remap directional controls, you have to use "System Settings" to remap menu inputs from the main menu, and this will also apply to character controls ingame.