Quick update: unfortunately using the Steam configurator doesn't work super well with this game, since mixing keyboard and controller buttons causes the game to pop up "new input detected" anytime it gets input from one to the other, and it seems like the gamepad buttons are being detected regardless of if I'm overriding them :(
The controller UX stuff is pretty slick honestly, and it would be great if the controller already worked correctly, but once you want to use fiddly configs like this, it kind of falls apart a little... I think other games have worked around this by giving you the option to disable controller inputs, along with choosing your button prompts manually and stuff like that.