I don't think the right way to clarify this problem is by looking at it terms of first- and second-level desires. I think you need to turn it around and see it as a matter of what 'true self' means.

If people say that the desires you "endorse" on the second level are most reflective of your true self, they're wrong. This is because what we take to define our true selfs is based on different criteria, and those criteria define it such that people's second-level desires don't always match up with what we taken their 'true selves' to be, as in the case of Larry.