I've skipped ahead and haven't read beyond colinsmom's post... (I'll return to add to my post if needed).
Connections is what I would recommend over K12 for gifties grades 3-8... reason being that they have effectively got a gifted pull-out which is the real deal with true ability-grouping and live instruction with peers, and has outside work (homework, essentially) that involves higher order literature analysis and synthesis.
K12 offers... hmmm... acceleration through the regular curricular offerings.
One other advantage that Connections would have for you is fluidity. Math is decoupled from the rest of the curriculum, so that would be an area of individual placement, effectively. She could effectively use the Connections program as a "bridge" to accelerate a year, and not have to actually "skip" anything. It would be superior to pure homeschooling in two ways: a) it retains a public school transcript, which makes the entire "grade-skip" discussion a moot one once you return to a local school, and b) while it can generally be completed by most GT kids in about 2-3 hours a day, it also strengthens the 'standard' skill set that schools expect, so homeschooling wouldn't worsen any extant asynchronies. (We found that was a real problem in homeschooling-- my DD could and did rely on preferred methods of learning and expression, which allowed her to leap ahead in some areas and lag in others.)
Compacting and accelerating like this is what we did for 4th-5th with my DD, by the way.
Adding:
It also doesn't mandate a skip (as in, a change in actual grade) since "placement" is a separate thing entirely with Connections. That is, a 7th grader can be taking a couple of high school classes with them and not BE a high school student, if that makes sense. I understand your concerns about a second skip. The Connections program would be a solution to a lot of your problems here, in my opinion.
Last edited by HowlerKarma; 06/29/12 09:52 AM.