My son had someone in his class who had already done 5th grade at his home school, having been skipped, but when a 5th grade slot opened up at the GT school he took it and "repeated" 5th grade. It was great for him and if only . . .
I also wonder why they haven't put your son in the GT program if they thought he needed to be skipped early on. Their decisions seem very inconsistent here. Many teachers confuse "gifted" and "high achieving" as well as "gifted" and "accelerated."
The greatest advantage my kids have had being in a GT program is the social part of it, being around kids like them and being appreciated for their "weirdness," having kids who are good at sports and kids who stink, but that not being the way they measure each other. The academics are nice too, but mostly because they don't do worksheets, they don't teach "3 times, 3 ways" (a great teaching strategy for most kids) etc.
I think you're asking the right questions right now. This seems like a good age to get some testing done and decisions made and hold the school accountable for correct placement.
Good luck,
benny