Sounds a nightmare but I think it was good to make a GP appointment, and at least you can say you've done that at the meeting.
I also think DS should be at some/all of the meeting. He needs to appreciate you're having time off work and that it is serious. Otherwise he can just pretend it isn't happening. What are the ongoing consequences, could you be fined etc, he really needs to know this.
I wonder if you could speak to the school about the policy for calling parents if the child is feeling ill, and having a parent come collect them. If this is all stemming from a genuine anxiety over feeling unwell at school and not being able to go home, then putting something in place where the school ring you and you have to leave work to collect him, might just reduce that. Then, if your DS is still wanting to stay at home of a morning, there's no excuse for him to do so. So if he's actually been sick at school, then that's a trigger for a call. If he has a bit of a cold, could the school allow him to take a pain killer (and have them issue it so it's recorded) so try to reduce the unwell feeling, after all, we'd take drugs at work if unwell. If he's feeling sick all the time then that clearly needs addressing via the GP, either it's stress related (or similar) or is something more physically wrong.
Then have some consequences of still not going to school once you have a clear understanding of their sickness (and going home) policies. Ultimately, the enforcement officer might be a way forward or a childminder. As others have said, the embarrassment of the loss of independence seems to have helped other teenagers.
I do wonder if it's a lot of crying wolf that has scuppered his chances of now being believed and therefore not calling you when he's been genuinely ill. I also think this needs talking through with him. If he's going to be ill and off school (or asking to go home) at the drop of a hat, when he really is feeling unwell, he's not going to be believed, or they won't appreciate it's more serious.