Let me preface this with the fact that autism is not one of my areas of expertise. So perhaps others will respond, as well.
But having said that, you can ask for anything in the IEP that you feel is necessitated by his disability and is affecting his access to an education. I would think that since he is already in a self-contained environment that the school would be receptive, especially since you are covering the cost. It might depend on how his educational instruction could be handled if he only attended half days. But it would be worth a discussion, in my opinion.
If the school district is not receptive to this, you may need to get data showing a need. You don't state where you are at in the IEP process, so I don't know if that would mean requesting a school evaluation/FBA or an Independent Educational Evaluation/FBA.