How can I raise the quality of this illustration?
An illustration with better workmanship will often attract the audience's eye over a poorly crafted picture. Even if an illustrator has a strong initial idea, the execution of that idea determines success of the illustration. In fact some illustrations succeed over others not because they have more thought put into them, but rather because they are better executed. The execution of the illustration validates that illustration to the audience.
A foundation in fine art should never be used as an excuse to override the customer's preference. If a disagreement in taste occurs, it is the illustrator's responsibility to offer both variations for the customer's examination (if time allows). While fine art helps validate the illustration in the reader's mind, there can be taste differences that do not change the illustration's effectiveness.
Because of my fine art education, I look at illustrations differently than most people. I look and see if the composition looks complete with both value and color pattern, and whether the major shapes in the illustration go well with each other. I also know how painterly to be and when to hold back on the texture to preserve the clarity of the illustration. All these subtleties only add strength to what's illustrated.