TheWonk;
I am so impressed with your post. Your daughter is very lucky to have you.
I have two aspie boys, and a very socially popular NT daughter who is now almost 16. Although I was a fairly popular girl when I was a teenager, since I've "matured" I have adopted a lot of aspie characteristics (don't care about fashion, I appreciate smarts over popularity, etc.), and since I am not dressed "cool" like many other mothers in our area, or I am not skinny, I've often wondered if I embarrass my daughter. I think that I have in the past, but I have learned over the years to just make myself scarce when her friends are over. ANY teenager wants that. You don't have to be an Aspie parent to embarrass your kids. Apparently that's an "equal opportunity" kind of a thing!
Just provide the drinks and snacks, make sure all is prepared for the sleepover (music, videos, whatever she wants), and then go to a different room and only come back into her room if she asks or if there's an emergency.
Now that my daughter is almost 16, she is beginning to enjoy my company with her friends. We just went shopping for something school-related with a friend tonight, and all three of us had a great time. My NT daughter actually ASPIRES to some aspie characteristics because she enjoys her brothers and her father so much, and definitely seeks out friends who have them. She considers people like this as superior. That day will most probably come for your daughter concerning you, where she will consider you as the measuring stick, and other people will fail by comparison. I think that any mother who is this sensitive to her daughter's needs is exceptional -- again, she's lucky to have you.