I'm not always convinced that the social skills aspects of staying with peer groups are as great as they sound. If you are easily ahead and enjoy learning, you are often considered in a slightly different way by your peers anyway. Not in the 'nerdy' sort of way that happens later on in school, which IS more a matter of social skills, and it's important to learn to get on with similar aged peers regardless of whether you like different things, but in a more subtle way in the early years - you are just seen as being like an older child to them. In early years, other children would come to me to have something read to them, I was always the one who did the peer tutoring and the helping and the explaining. I don't know that it helped me learn anything better by explaining it, as I did have a perfectly good grasp already, but I enjoyed being the helper, and was good at it, always did peer tutoring programs, etc. Never got taught anything extra myself, really, just picked up what was done in class without needing much instruction, and then could help the others. And that was all fine, except that I wasn't quite seen as a peer by the other children. They liked me, I liked them, but we had different interests, and I had a different role, somehow, and didn't always get to play with them like age-equals as a result - I was someone that you came to for help, or whose attention they might have wanted in the way that you like it when an older sibling comes to play. I was seen by them like I wasn't part of the same class, and it does affect social interaction in a subtle way. I was 11.5 months older than some of the children, but it felt like more at times. And it just made me very different.
I don't know that moving up a year would have helped either, so I'm not saying that is necessarily a good solution. Just, that it's not always such a given that keeping a child with age-matched peers will result in normal social interactions anyway. You ARE different if you are far ahead, and more than just academically.
I know a child who is also several years behind academically, and she is also not really having normal social interactions with her peer group. They know she is different too, and it's not that they are trying to exclude her or treat her differently or anything, but she simply fits in better and prefers to play with those who are somewhat younger (not as young as her academic level, of course, but a year or two younger than her actual age group). Her academic difficulties have also ended up keeping her interests in some ways at the level of a slightly younger child too. So she also doesn't have entirely normal friends in her year group, and ends up not really fitting in academically or socially.
No easy answers, but it's definitely not the case that a child will just automatically fit in with the social group of their age-matched peers, especially in primary school. Perceptions of that child as 'a helper/teacher' or 'someone needing help' mean that they can take on those roles and just end up being treated differently anyway.