For a comprehensive evaluation, a good place to start would be the psychologist who did the cognitive testing. School psychologists, clinical psychologists, and neuropsychologists are all qualified to do this kind of evaluation; their facility with 2e evals is primarily dependent on their individual training and clinical skills, rather than their specific licensure. You could have such an evaluation done at no cost to you by your local public school, or done privately at out-of-pocket cost (depending on your insurance, you may be able to receive partial or full reimbursement by seeking prior authorization through your primary care physician). Some families have good experiences with this route, while others find that the goals and perspective of a private evaluator are more suited to their needs. (Full disclosure: I'm employed as a school psych. I've certainly seen the full range of quality in evals from both school-based and private psychs.)
It's best to start from a referral question that emphasizes his functional needs, rather than searching for (dis)confirmation of a diagnostic hypothesis. However, some exceptionalities that can affect written expression include dysgraphia, motor coordination delays, executive function deficits (e.g., attention, planning, organization), vision (acuity, tracking/convergence), expressive language delays (this can be very subtle, with inconsistent performance often depending on the topic or the nature of language expression demands), or anxiety.
