聡明 almost always modifies a person.
賢明 tends to modify a decision or strategy (判断/選択/戦略/etc), but it can modify a person.
When they describe a person, I think 聡明 focuses on one's intelligence (e.g., "being good at debates", "being able to understand difficult math concepts"), wheres 賢明 focuses on one's judiciousness (e.g., "makes a good decision when in trouble").
I guess the difference actually mainly comes down to 賢い and 聡い
I think you are over-analyzing. 賢い and 聡い both mean "clever/smart" and I don't think there is a big semantic difference. The biggest difference is frequency; the latter is fairly uncommon today, and you almost never hear it in modern conversations.