Hi Leahchris,
The "never does homework" is a warning sign for me. My child with AS had issues with homework in the early years-- he felt that it was an unwarranted intrusion on his free time at home, and he resisted with all his might. If we had homeschooled, it would have been very difficult.
Our therapy team has also recommended not homeschooling, because so much of being in the workplace is learning to be flexible, take direction from others, be patient when there's a slow time, and do the assigned tasks when they're due. The team felt that school would be hard in the short term, but the long term gains would be real. DS is now finishing 5th grade, and we see the value of that very clearly. There is no doubt that had we homeschooled, he'd be further ahead academically, but our willingness to flex to his preferences would have allowed him to be more rigid, making him less fitted for the workplace in the long term. We feel this was the right call for us.
What accommodations and supports are in place at school? It seems likely to me that you can adjust things so that he's less anxious, possibly through teaching him skills and providing access to respite when he needs it. (A "moment out of class" ticket can be a huge gift for an anxious kid-- just knowing he can leave and regroup if he needs to makes it less likely that he'll have to.)
And how are you treating the anxiety? We found that our child did much better on a combination of an SSRI (for the anxiety) and an ADD medication (for staying on task). Cognitive-behavior therapy is also very useful for learning to identify anxious or rigid thinking and combat it.
DeeDee