Thanks so much, everyone. I appreciate the advice and commiserating! It's glad to know this is similar to what others experience.
With regard to sports- I have made it a point to keep her in a team sport every season since kindergarten (she's in 3rd grade now). Several reasons for this...she would be perfectly happy reading a book in her room for hours at a time and I want her to get out and be physically fit; I hope she will find a sport she really likes and want to continue into the upper grades; I have felt, particularly in our community, that it is important for her socially. She has played on teams with the same group of girls from school pretty much every season. I feel like this keeps her engaged in something all the kids can relate to, instead of her unique pursuits, like Greek mythology. It gives them a common bond. She is also more motivated to join a team right now if she knows her friends are playing. However, as I see more of a gap developing with her and her agemates, I wonder how long this will be a factor.
The problem we have with most team sports is she can really take it or leave it, and just doesn't try that hard. She's had the same soccer coach for years who has said that, when she tries, she's as good as any girl out there. BUT she is too lost in her head most of the time to really focus and care. Same with basketball and lacrosse. I put her on the swim team last summer. She's a good swimmer and I thought that was a nice mix of team and individual sport. However, that is not to her liking...as she says, she likes to swim, but not have people tell her what stroke to swim when...or how many laps...and she doesn't like the pressure of everyone watching and cheering for her during her heats

Right now she is in volleyball, which she likes a lot, for the first time that I remember, so that's great. She has mentioned karate/ martial arts several times. Maybe that would be worth checking out.
I will look for some of the books mentioned. Also, I am curious, Pru, about your connecting gifted programs to reduced anxiety...could you tell me more about that? In her private school, there is no gifted program. But as a teacher in the public school system, I'm not sure that her options there (twice weekly curriculum extention unit, math 2 yrs above grade level) would be worth what we would give up leaving her current school.