Call the school and talk to the admission's coordinator openly about your pyschologist's opinion that Menlo Park would be helpful to your son and about the challenges you are facing, see what ideas they have.

On the lunches, it sounds like the current school has a free or reduced lunch option but that is not available at the new one? The new school is public too, they must have experienced the need for lunch assistance before.

You may have a local food bank, they will often provide free bread/peanut butter, milk you can pack in a thermos, etc, or just general food supplies that will lower your other food costs enabling you to balance out the cost of lunches. Or you may qualify for food stamps or other food assistance, in most states you can call 2-1-1 to see what you are eligible for.

Polly