Grest advice from others! I would agree with you that just telling someone who's anxious 'just calm down' is ineffective. You cannot logic out of anxiety because anxiety is actually a physiological response. Anxiety is our primitive (and effective) fight or flight response gone awry : rapid heart rate, shallow breathing, tense, restless, reactive, and generally uneasy. It feels awful - and thus those that experience intense anxiety will do anything to avoid it.
Before an anxious episode begins, you can help gameplan triggers (which you found like you are already doing), but don't try to take this approach in the midst of your DS' hyperarousal...he can't access that part of his brain on full fight or flight. Instead, focus on the physical reactions of anxiety. Help him slow his breathing, relax his muscles, slow his heartrate (kids think that's amazing) through some simple relaxation exercises (there's many ideas online). You can slowly increase his ability to tolerate anxiety in tiny steps (ie: 3 minutes without an extra sweater and gradually work to 15 minutes) while helping him stay as relaxed ad he can.
A good therapist/psychologist can help you with this approach. Also...though it may provoke it's own anxiety, I usually suggest clients get a thorough physical exam initially as some illnesses can trigger anxiety (hyperthyroidism, asthma, side effects of stimulants, steroids, antihistamines).
GL