We switched our ds11 from public school to private gifted school starting 5th (middle school started in 5th at this school). We had him shadow at the end of 4th. He was very nervous about it but it took all of 10 seconds and he was pointing to me to leave he would be alright. It went wonderful and we are now in our 2nd year.
Its a long road you have time on your side to plan your switch if it comes next year or even the next.
Our ds knew that the private school was the place for him. He took the EXPLORE there in 3rd grade the year before and we walked around and introduced ourselves to everyone (head of school and some teachers) so it was not totally new.
Does the new school you are looking at have anything going on that you could participate in, contest, fun nights anything that could break the ice for him.
Keep us updated.