We have been happy with Bellevue School District gifted program as well.

I remember Bellevue School District having summer testing last year for students who moved to the district after the January testing time. I couldn't locate that info in their website, but might be worthwhile to contact with them via email. http://www.bsd405.org/about-us/departments/student-services/gifted-education/testing.aspx

As far as private schools, you can also look into Open Window and Seattle Country Day. I believe they continue until 8th grade. I also heard good things about Eastside Prep. Most of their application deadline passed though, you might want to directly contact them for any availability.

Best of luck...