What is their definition of giftedness? It sounds like maybe they are looking at something like above the 80th percentile. Very bright but not needing much out of the ordinary.
Sorry I don't think it is going to work. They will say "we have all gifted children here and they don't have a problem" but your children hit the ceilings on some suggest so are probably at the top end of highly gifted at least. I read somewhere the other day that there is as much difference between 160 and 130 as there is between 100 and 130. My son tested at 158 and he couldn't read before school (some words not reading). Good luck let us know how it goes.
Oh and if you sons are anywhere near as exhausting as mine well done for surviving this far.