Perhaps it would be worthwhile to have a conversation about the need for balanced development--online school certainly can address many, if not most, of his academic needs, but it won't do much for his social development (which is a need that every young person his age has, regardless of the presence/absence of social anxiety). In-person school contributes, ideally, to both types of development, so if he wants to go to online school, he will have to find or agree to another mechanism for natural social development. E.g., a club, sport, community service, job, etc. But it won't have to be 5x6 hours, it will separate social interactions from academic learning, and it can be an activity/group of his choice, which might lower the stress level, and increase his likelihood of success.
