My idea is to 'roll' back onto my rear foot to effect of avoiding my opponent's cross, rather than attempt to interpose my shoulder into the path of the blow. The motion itself pulls me away from their punch and loads up my right hand.

If you're standing square, as is usually the case with fighter who stands in a peek-a-boo guard, you can't perform the shoulder roll effectively. To begin with, this stance prevents the natural movement of the shoulder roll, and there is a greater distance to overcome.