I'm Canadian so I can't really answer your question, but I just wanted to caution you in thinking that somehow using a school-style curriculum at home could be the answer to not having access to gifted programming.
First: in my observation and experience school-at-home seems to be viewed by he regular school establishment as being somehow cheating since it's not a fully rounded-out school experience, and they make up for the lack of, oh, group project work and chalk-and-talk teaching by demanding significantly more busywork than school kids would get. My eldest dd and her friend once did identical courses at the same time, one school-at-home, the other in a bricks-and-mortar school. What would constitute a 10-minute group discussion in the classroom would be turned into a research and writing assignment that would take an hour or two in the school-at-home version. I also think that in the classroom teachers are trusted to keep an eye on student understanding and if maybe 5% of the time some of the students don't seem to be getting something, they'll know to backtrack and reinforce. With school-at-home, with no teacher in the room to make those judgment calls, it's like the curriculum writers want to ensure that there's enough teaching and reinforcement there that the 5% risk that a student won't get something is reduced to less than 1% by repetition and reinforcement.
So there's that. And then there's the issue that simply moving more quickly through a standard curriculum often doesn't address the different ways gifted kids learn. My dd11 is doing preCalculus right now as a homeschooler, out of a standard school workbook/textbook. So she's radically ahead, by 4 years or so. Both of us feel it's a good level for her and she's doing well without much effort. But the thing is, she still finds that the explanations are sometimes too cookbook-ish and stepwise. The level of challenge is about right, but things tend to be presented in tiny incremental steps that bog her down in the details of executing algorithms, rather than showing her the big picture first and then drilling down into the details.
A great explanation I once heard about accelerating gifted kids through a standard curriculum approach was of a cheetah travelling with a camel train. The cheetah, traveling at the back of the camel train, is frustrated by the pace of the train and is bored and annoyed by being held back. Finally the camel drivers tell him okay, you're a cheetah, you're faster: go up and join the first few camels. The cheetah is thrilled because the first few camels are way up in the distance, so far ahead that he can only see their dust. He runs like the wind, excited to be there with them. The problem is that once he gets there the first camels are moving at exactly the same speed as the ones at the back.
So yeah. I don't know why you're looking to do school at home, but it certainly wouldn't be (isn't!) my choice with gifted kids.
Sorry not to be any help with K12 vs. Connections. Hopefully someone else will pipe up.
Miranda