If homeschooling, as someone else mentioned, isn't something that works for your family, would another school within the district be more accommodating? I never intended to have my kids move around as much as they have, but we've been in two districts, homeschooled, and tried a charter school in order to get dd13's needs closer to met.
The year that dd skipped, 5th, wasn't one I even had to advocate for. I called around to potential middle schools (6th-8th) when she was in 4th to say, 'here's what I've got, what will you be able to do for this kid when she gets to middle school?' The GT coordinator at the middle school she wound up attending listened to the test scores we had (IQ & achievement) and what else I had to say about dd and suggested as her first thing that we send her right away, skipping 5th. We went through the IAS with her current school at the time and the middle school and, while the current elementary hadn't been the ones suggesting the skip, they had to admit on the IAS that she more than met the requirements.
The thing with the IAS that I've found to be a bummer is that it is pretty subjective. If the school is strongly opposed, they can fill out all kinds of things like work habits, social skills, etc. to put the kid in a poor light.
