I only have experience moving my kid our of our local district mid-year due to bad school fit in 2nd grade, so this is not directly on point. In my not so humble opinion, though, it makes little sense to move a GT kid when they are in a good fit situation. It is so hard to predict whether any school situation will work well for GT kids, so I'd stick with the school you know and like. (And if were me, I probably wouldn't plan on changing schools next year either, and keep the new school as the backup plan. But that's just me.)

My kiddo has lots of friends in the neighborhood, of all different ages (so they wouldn't have been in his class even if he did go to the local school).

I would say there might be some benefit to going to a school mid-year if the next year is a big transition year (e.g., if your kiddo will be going to a new middle school next year, then it might make sense to meet some of the kids she would be going there with if they will be different from the kids in her current school).