I'm probably going to just reiterate what others have said, but I doubt that either a gifted school or a gifted program in a public school is going to be the best fit for your children. My kids are not as advanced as yours and fall more into the HG+ area (and one of them is 2e), but your options sound similar to our local schools except the only semi-local private gifted school closed a few years ago.
Like Grinity mentioned, programs aimed at gifted kids in public and private schools are usually looking @ about 5% of the population or even more if they are doing what we see locally to me. Here they look at kids who are in the top 5% in any one area, so a 95th percentile score in any area (reading, math, writing, etc.) plus a 95th percentile score on any one area of a group test like the CogAT or OLSAT (again, verbal, non-verbal, quantitative, etc.) will qualify you for a GT and possibly placement in GT classrooms. They also take kids with high achievement scores into those classes even if they don't have ids b/c they don't hit the requisite group ability test score.
I'd start by looking at what qualifies as gifted in your local public schools. The broader the definition, the more inclusive, unfortunately the less likely it is to meet the needs of your kids.
I'd also give a call to the GT coordinator for your district and the admissions or curriculum person for the gifted school and ask them how many kids they have like yours. If they tell you lots, I'd look elsewhere b/c it is more likely that they don't understand the rarity than that they have tons of PG kids. I recall a conversation I had w/ a GT coordinator for a local school regarding my 2e child when we were looking at changing to that school. I didn't even ask how many kids they had like her but the coordinator volunteered that she had lots of kids who were gifted and just like dd (dd has a 99.9th percentile GAI on the WISC-IV (IQ) and ADD). Knowing the school from some prior experience there, it told me more about the coordinator's lack of understanding of what that meant than the population of the school being full of HG+ kids.
Other options would be looking at homeschooling if that is an option for your family. Do you have a homeschooling cooperative locally? Something like this was my dream to have locally for a long time:
http://www.voyagersinc.org/wiki/bin/view/Public/WebHomeYou might want to contact some of the IL groups on the Gifted Homeschoolers forum:
http://giftedhomeschoolers.org/giftedresourceselsewhere.htmlEven if you don't go the homeschooling route, they might have some resources for you and give you some good social connections.
