Welcome back!
First off, I definitely do not recommend prepping children for the CogAT, or any other aptitude or cognitive assessment.
Secondly, his existing test scores do not suggest that visual-spatial abilities are truly an area of deficit. He did quite nicely on Visual Puzzles, which is probably the best predictor of visualizing holes in folded paper. Block Design may be a low estimate of his spatial abilities, based on your information on fine motor skills from the NEPSY.
Thirdly, if the school system's GT programming is designed for those children who score well on their entrance criteria, then the benefit of attempting to enter students with marginal or clearly nonqualifying scores is questionable. GT and academically advanced programs historically involve a significant increase in volume of work, which may or may not be detrimental to a student with no more than average processing speed, with low fine motor skills (which often translate to writing challenges), and who is already struggling with stress. Knowing nothing about the program in question, I can't speak specifically to the risks in this case, but I would certainly encourage a thoughtful process.
It may be that the more important concerns to address are those related to the suspected disability, which I see that you are already in the process of doing.
