Re physical buttons: I always wonder why there are no "modal buttons" in cars. E.g. 4 buttons on the left, 4 on the right.
The ones on the left open "submenus" the ones on the right trigger an action from the submenu.
Can be visual, but should not depend in the GUI to keep up.
Examples: Left 1 puts you in the audio menu, Right 1 increases volume. Left 2 puts you in the cruise control menu, Right 1 activates.
Humans are actually pretty good at learning simple patterns like that.
4x4 gives you 16 functions on the wheel. Going one level deeper (left, right, left) would give you 64 possible results. That should be enough to cover all bases.