The antonyms for the phrase "more unmethodical" could be "systematic," "organized," and "methodical." These words are used to describe a particular way of doing things, which is the opposite of unmethodical, meaning without a proper system or plan. Being systematic means following a methodical approach with a set of practices and procedures that aid in achieving desired outcomes. It is characterized by order, structure, and organization. On the other hand, being unmethodical means disorganized, chaotic, and haphazard. Therefore, using antonyms like systematic or organized can depict a more efficient and reliable approach towards completing tasks.