Hi Jtjt - welcome! I am going to second kcab's recommendation of filling out the Iowa Acceleration Scale form, as it considers many different factors in determining whether a child will be a good candidate for acceleration (full grade or single subject). Each section of the IAS gets a score, and the total of all the different sections determines whether a child is a good candidate. The social part is just one section.
As for full grade skip versus single grade skip, with some kids with really high scores like yours, sometimes it gets more and more difficult for the teachers to differentiate. Most of the time, pace continues to be an issue for these kids, and it's easier for the higher grade teacher to differentiate one or two grades up than it is for the lower grade teacher to differentiate 2 to 3 grades up.
Our experience is that our son went to K with agemates, and had differentiation including 2nd grade math. He then skipped 1st grade, and due to miscommunication, DS didn't start with 3rd grade math, but rather started over on 2nd grade math he had already done (so make sure you get lots of expectations in writing!) Like your DS, our son's handwriting was terrible. He had not wanted to learn to write before K, and he came out of K knowing how to write, but very poorly. In addition to the wrong math after the skip, we found that the pace was too slow for our DS across the board, and we took an opportunity to send him to a school for HG kids, where the fit was great. His handwriting is still awful, but the school takes kids where they are and don't put a lot of focus on the weakness. DS's writing continues to improve, but I will imagine he will still be the worst in his class. I don't think that would have changed even if he weren't a year younger.
Your son's K teacher knows how the kids are in your district, so I would take her word for it when she says that your DS would do fine skipping 1st. Many 1st graders are still learning to read, and some people find that it's a really hard year for GT kids because they do a lot of waiting.
Are you switching schools within the same district? If yes, I would recommend documenting all the acceleration that the recent school provided for your DS (going up to higher grades for certain subjects, etc.), because in my experience there is sometimes a great lack of communication during a school change, even in district.
If you can afford to get a consult on your DS's scores, a professional's advice as to your DS's schooling can be very helpful. But rememember that whatever you decide, it is not the end of the world if it doesn't work out 100%. School situations can be changed.
