I noted in your OP, Helianthus, that your son exhibits various symptoms of sensory defensiveness, yet the only accommodation you mention that he's being provided is a 20 minute recharge at the end of the day. I know that, as an adult with auditory defensiveness, a day with few opportunities for quiet rest is problematic. Could your son be given an option to withdraw from group activities outside the gifted pull outs at other times of day?
Another consideration is that he may, biologically, not be ready for full days without a nap. As a 4-year-old, I needed a 1-2 hour midday nap and was in half day kindergarten as a result. How does the school day map to his natural circadian rhythm? Is he energized in the morning or sluggish?
Just to throw out another consideration, how much are junior teachers paid where you are? Would it be affordable to hire a teacher to (part-time?) homeschool him for you while you and your spouse work? (Some families share a homeschool teacher, and this can make the option potentially more affordable than private school.) You could effect the grade skip yourselves, and have achievement tests done subsequently to validate your son's achievement for a further skip down the line.
