your daughter did well. She would make the cut on most gifted programs that usually have a cutoff around 130. Her GAI just makes the cut for DYS, so that is really very strong. However from my experiences here in Long Island, the school districts don't really know/care about GAI. I hope its different for you. So you might not get a lot of reaction from them with the 130. Beyond that i can't analyze the scores too much- i'll leave that to others who know more. But the fact that she's ten eliminates the whole "too young to be accurate argument"..
about moving,I also live in Long Island and have a gifted child and a child with autism (who we now know to be 2E). We moved to HHH district to accomodate my autistic child and is "pretty good" for gifted but since my daugther is only in kindergarden the program hasn't started yet. They are absolutely unimpressed with anything i tell them about her scores, etc. from a private psychologist. I've found that the word "gifted" is a dirty word and you get absolutely no where using it. Stick to "high achieving" etc. and talk about "differentiation" instead of "gifted program".
Like me, you also have to consider accomodating both kids if you switch districts. Have you considered LISG? I think they require a 130. I've heard its a good fit for some, though my daughter spent the day there and did not go for it. ..If I had it to do over I would probably go to Sysosset, as i have a lot of info now that i did not know when i moved three years ago.