You also have a right to request that the local education authority (public school district) evaluate your child based on your list of concerns, at no additional cost to you (beyond what you're already paying in taxes!). In his case, you've listed academic and developmental concerns, not only gifted concerns, so the school district would be obligated to evaluate him in his areas of suspected disability. To do that, you would write a letter to the director of special education/special services/pupil personnel services (usually it's one of these titles) in the public school district in which you reside, stating your concerns (written language skills, social-emotional development, sensory sensitivity, rigidity, in combination with highly divergent academic skill levels), and request a comprehensive special education evaluation, including cognitive ability, academic achievement, autism measures, and maybe occupational therapy and emotional assessment.
This avenue is highly affordable, but also fairly variable, in the quality of evaluation you may obtain. I'm in the field myself, and know many competent assessment professionals who work for public schools. But I also know people I wouldn't send my own child to (both in schools and in private or hospital clinics). Some families have also had success with asking the schools to do the basic cognitive and achievement portion of the eval, and then filling in the remainder of it with a private neuropsych. I would suggest looking for personal referrals/references, and conducting a thorough interview of the person prior to committing to an evaluation. I would echo the importance of someone experienced with 2e.