Here's a list of private gifted schools in MA:
http://www.hoagiesgifted.org/schools.htmThere's a ton of other private schools in MA; some of which are top in the country. However, I don't know what they're like for gifted children.
I wouldn't be discouraged about applying for a private school for the fall. Try it. People move; jobs change; things come up so you never know if a slot opens. And with the economy, there may be more slots than in previous years.
I enrolled my son mid-year as a pre-k student in two gifted schools, after the first gifted school didn't work out for us. So yes, it is possible. Some of the gifted and private schools have open enrollment.