The antonyms for the phrase "most rough hewn" are smooth, polished, refined, elegant, sophisticated, and cultured. Smooth signifies the absence of roughness, while polished denotes a highly polished state. Refined refers to something that has been delicately handled, while elegant suggests a sense of class and sophistication. Sophisticated implies a high level of intellectual and cultural development, while cultured points to a high level of cultivation and decency. All these antonyms indicate a level of polish and perfection in a material or an object, which is the opposite of rough-hewn, which connotes a lack of refinement or sophistication.