Yup, Perceptual Reasoning will get him in. By Dottie's calculations his FSIQ will get him there too. While GAI is a better number when it comes to his abilities, it's not what Davidson accepts. Have the psychologist give you full report with all scores even if she doesn't care for them and apply to Davidson. It sure is worth it.
I am another homeschooling mom (DYS 6) but some people can make it work just fine in public schools. Skip to 6th or 7th would be a stretch but 2 year skip and perhaps additional subject acceleration can work wonders for him. Do you have grade equivalents for his results? One thing to keep in mind is that the grade equivalent talks about an average x-th grader and whatever grade you will move your son to you don't want him to be average. You still want him to be close to the top of his new class.