I understand how difficult it is for you to make this decision; I hope my experience can help you. My Ds1 was advanced academically as a child, when he started kindergarten he read at a fourth grade level and math was at a third grade level. He tested into the school gifted pull-out program (waste of time), and at the time I thought it was fine. I did not pursue any sort of grade acceleration and he progressed through elementary and middle school with a straight A average. He never studied; school work was easy for him, he received a lot of homework, but it was always easy. We moved to a district that had one of the best high schools in the country, and the average student in that school performs above level. Now Ds1 had no study habits whatsoever, had never really been challenged, as a consequence, high school was a disaster. I finally pulled him out of school at 15, homeschooled him for a year, had him take the SAT's, ACT and subject tests, and he is in college now (at 16). His study habits have improved, but I strongly believe that the lack of challenge during his formative years were detrimental for his academic growth, and I don't think he will ever recover. If his social life can be managed, I would strongly advise you to do the two year skip. That way he will be challenged, it will make him happier, raise his self-confidence, which may in turn make him more social. If the school will allow him to do advanced work with his age group, that would be great, but that's not to be trusted 100%. Ds1 second grade teacher allowed him to do 4th grade math and 4th grade reading, which was great, but when he went to 3rd grade (same school), he did 3rd grade math and 4th grade reading along with his entire class (every grade had reading 1-2 years above grade level). So if the school will do in class subject acceleration, try to get it in writing.
