Have you checked the SD website on details about when they do testing for gifted programs? I don't know where in WA you are. but in the Seattle area they seem to have similar, but not equal, procedures. For the ones in our area, parents or teachers can recommend for testing, then they go through subsequent rounds of testing. Most of the time, you have to sign up way ahead of time (in the fall for testing in the spring, for starting the next fall).
I don't think Davidson would accept those scores. Also, if the kids qualified for the program you could be sure they are gifted, but would have no real idea of how (areas) or how much (level). Also, gifted kids sometimes do NOT qualify because they don't do well in a group setting, or got lost in the verbal directions....
