More importantly, you can't just infer n-th order desires from n-m, n>m>0 order desires.

I am starting to agree with other posters that the whole construction may not map reality too accurately

I agree. Generally people don't have very high order desires. Discounting the accuracy/usefulness of the notion of ordered desires was the entire thrust of my original comment.

First , these two statements are 2nd order and 3rd order respectively

This is still a matter of interpretation based on wording. In my original phrasing it's more apparent that the desire is first order. My set up was that Larry "experiences genuine disgust when he thinks about homosexual acts", the intent being that his reaction to homosexuality is involuntary, and his desire is simply to avoid that unpleasant reaction. This is first order.

I'm not claiming the order can always be reversed. I was just giving a particular construction where it could.