Interesting idea, thanks for that. I see what you mean about the joystick use being more intuitive, particularly with the direction. Challenge with that is to highlight the row/column to be moved - it was pretty difficult, technically, to display all of the colours in 3D as it is.
Maybe it could be implemented in one of two ways:
(1) The specific section you are currently on, could blink back and forth between its normal color and black,, so that it should remains clear, where on the cube you are located. Black could be used here, because it's not one of the cube's standard colors.
Or (2) only the outline of the section you are currently on, could be displayed in black (instead of the normal blue). Even that alone, should actually be sufficient, to make it visible to the player, where on the cube he is currently located.
Perhaps one of these two approaches could be implemented somehow? Unfortunately, I am not a programmer myself, so I cannot say exactly what's technically feasible and what's not. But I do think, that at least one of the two, should technically be possible.