Yeaaah I'll be the first to admit the game's keyboard controls aren't very good! That's why we threw up the big "playing with a gamepad is highly recommended" message before the game starts. I am sorry about that! We're still working out new solutions for controls, including one that includes Mouse+Keyboard together (which is looking promising). In the meantime, maybe you can scrounge up an Xbox controller?
I'm not sure of to whom you were referring, but I do have an Xbox controller (which my SO uses). It's just imperative IMO in general game design for all menus to use arrow keys, Enter, and Escape, regardless of the actual player controls.
This game could totally use Overcooked's method for two players on keyboard! It uses WASD + Left Control/Shift/Alt, and arrow keys + Right Control/Shift/Alt, along with a couple of other keys.