If it's any comfort, I hear this story all the time, and it's totally age-appropriate.
We have had some success with getting students to use their accommodations by taking some of it out of their hands. For example, the teacher simply gives him only the multiple choice portion on day one, and then gives him the short answer portion on day two.
We also encourage teachers to become comfortable with UDL (universal design for learning), allowing many students a menu of low-level accommodations, regardless of disability status, which not only benefits a wider range of students (and encourages deeper instruction, incidentally), but removes much of the stigma of using accommodations.
I've had many, many conversations with students about the difference between their performance with and without accommodations, and I emphasize that their work with accommodations is a better representation of their true selves than their unaccommodated work. It's not fair to oneself, or to other recipients (and, someday, beneficiaries) of one's work, to display only the cut-rate version of one's abilities to the world, rather than the full range.
Using appropriate accommodations is not cheating. NOT using appropriate accommodations is cheating yourself.
