My AuDHD son also had dysgraphia, dyscalculia and very low processing speed. A few thoughts:
1. It sounds like test prep is not the problem, but content mastery. He needs in-depth tutoring because there are obviously some knowledge fragments he doesn't control and it increases anxiety and disorganization during the test.
2. Does he have extra time? My son had 50% extra time at first, and then the school upped it to 100% extra time. His processing speed was measured at the 4th percentile, so it was sorely needed.
3. Does he have ADHD and is he medicated for it? My son needed to take his meds every school day to focus appropriately. If he misses questions and doesn't follow directions, then he might be inattentive and could benefit from meds.