Your last post rang minor alarm bells for me about girls with aspergers - it was the "more interested in setting up play than the actual playing", particularly in combination with wanting to play her games her way... I have a girl with Aspergers and she doesn't play "normally" and it has caused some problems.
I read it that way too. There is a difference (and a hard one to sort out sometimes) between people who are introverts with usable social skills, and those who cover up for social skills deficits using introversion as a way of not interacting.
Mountain, there are a few things in your description that sounded like your DD doesn't have the skills to play the way other kids do. Controlling others' play is something we often see in kids with Asperger's.
Obviously, it's not diagnostic-- just one thing to consider.
DeeDee
Curious, do girls with aspergers do better one on one with kids vs. a group of kids? We just had a play date yesterday at the park with a 10 year old gifted girl and she did great. I think if she is playing one on one she does much better. This is something her pre-k teacher noticed about her when she was 3/4 years old. She avoided groups of kids. Another thing the pre-k brought to my attention at that age is she didn't like to be touched. At home, however, with me she has always been affectionate.
The thing is-- this is absolutely normal HG introvert behavior, too.
(I realize this doesn't help you tease things apart.)
My DD definitely has a preference for one-on-one activities with others, but HAS the skills necessary to interact with a large group. If you list her quirks, she sounds
absolutely Aspie. But she's not-- you can tell within seconds of meeting her. Those quirks make her highly Aspie-compatible, however. Many of her closest friends over the years have been on the spectrum.

That might be an idea for you, actually. If your DD (or you) know any families with Aspies at similar academic functional levels, you could try setting up a casual social encounter and see how things go.