For me the most challenging aspect of the grade skip involved being really really sure that my kid wouldn't 'run out of smarts' down the road when school finally gets harder - so the above level testing, the individual IQ test, amd the Iowa Acceleration Scale Manual were a great comfort.
Starting a new school is a social challenge in general, and I've heard of things going both ways socially with gradeskips. Does your son have any dear friends at his old school? Are they also local or part of other social networks?
If the LOG is high enough, and there aren't 2E type problems, then one grade skip may not be enough. Go sit in your 4th grade classroom in your current school and check out the teacher, the flow of the day, how much abstract thought is involved, how the kids interact. It sounds like you can take the gradeskip at the current school for at least one more year, and switch to the new school (with perhaps another skip) the year after.
I would reccomend continuing to participate in the process of applying to the new school just to see where they would place him... I've learned as much from watching various school interpret my kid as from the IQ scores.
Best Wishes,
Grinity
