If the gifted teacher can give the mother, the special education teacher in the school, or the aide the topics they are going to cover in advance, perhaps someone could make structured independent worksheets on which the child can track the lesson, like an agenda or schedule. This way, the child can have order and predictability in the class, which will help him focus.
Another activity that is suited to kids with Aspergers is independent research on the computer or in books. If the child is given tasks to accomplish alone or with a single partner, it would be less stressful because the social component is eliminated or lessened.
The tried and true behavior management, stickers for on-task behavior on a timed basis (every 5 or 10 minutes) frequently works, but the teacher has to be into it. I would imagine from what you say that the teacher is not comfortable with changing her style to accommodate the child that much. Perhaps someone could make a sticker chart for the child with a space for each 10 minute interval and give the child a timer or a vibrating watch-timer. The boy could then self-monitor his attention.
The teacher could also try to give the child a specific goal-oriented task at various times during the lesson to keep him involved, such as handing out materials, listing information on the board (can he write and spell well enough?), typing notes on the computer from the teacher's board notes to make handouts for the class, helping with set-up for any projects or hands-on activities like moving furniture or dividing the class into groups.
Just a few thoughts. Hope they help.
G. Whiz Educational Resources, Author of Looking Glass Spelling and G. Whiz...I Finished My Homework!