I don't ever post on any forum, but your post is what I could have written just over three years ago, other than it was more personal reason for our daughter
If he is already diagnoised with an anxiety disorder, then any one saying that he should be made to do something that will increase the anxiety, and that will just make things a hell of a lot worse for both of you.
It's not about proving that he can do it and that it's not as bad as it seems, unless you have a child with these problems then you have no idea what it is like for them or their family.
My daughter has read your post and her words are that he isn't been naughty in the way he is behaving, and the reason that by lunch time that he is calmer and wanting to eat and play, is that he feels safe and is less stressed. these are the words from a child that has/is going through the same.
If he is becoming more distressed, then see your doctor again, and contact the school to say what you are doing, by keeping him at home.
there are other options about schooling, and there is more support out there aswell. Speak to your support worker from cahms. If he stays in the school then he needs support and a place or some one he can go to, when he can't control the anxiety/panic attacks, if the school isn't willing to help with this, then may be you need to look at the other options.
The day we decided that the best thing for us as a family, was to stop sending our daughter to school, that was three years ago, now she has tutoring with aotas, but will never attend full time school again, is under 24/7 supervision, but life is easier, there are still dark days and she does still OD and self harm but its getting less. She will have gcse's at the end of it all and the chance of having a normal life. She is receiving three different kinds of counciling and is now on medication, but if we had kepted pushing her to school then I really don't think we would still have her now.
Didn't actually mean that to be so long, just I know how hard it is as a parent to have to live with this, and at times its like no one has any idea how hard it can be.