My son is also on the spectrum and has the same social issues (probably worse actually, the kid actually told his therapist I was an alcoholic once because he thought it would be funny

), but don't let that deter you from eating in the main dining rooms.
DCL has a dedicated team for cruisers with special needs. Call the reservation line and ask to speak with the special needs/services department (they will give you the number) so they can add special notes and requests in your child's file. This way, the servers, kids club staff and room attendants are aware of any special tips or concerns you may have to help make sure your child - and you, can have a worry free trip.
They made sure we had a private table in a more quiet area of the main dining rooms. They put notes in his file so the kids club staff were made aware that our son does not like to be touched at all. They even put some notes in his file about his likes/dislikes so CMs could approach him about the things he was interested in. It was such a relief to us that DCL was was ready and willing to consider our son's needs. They genuinely seemed to want him to feel comfortable and welcome, which in turn, helped us feel comfortable.