Welcome - to the board and to the Chicago area. I'm a mostly lurker in the western suburbs.
First of all, if you think that something is "off" with your dd, believe yourself... there is. I have found over and over again that parents are really, truly, the best at diagnosing almost everything.
We have four kids, youngest is 8, oldest is 20. Dd20 is the one who kind of sounds like your dd. All are gifted, but she is the only one officially dx'd as PG. We had a full spectrum of tests done by an educational psychiatrist, but unfortunately, we waited until she was in middle school. We did it in response to a lot of anxiety issues. It was a long road - filled with outbursts, sadness, intensity, etc etc... the school RARELY saw the problem until high school, because she was a typical girl there: quiet, well-behaved, etc... They also didn't think she was all that brilliant when we first moved here - they didn't accept out-of-state testing, and I think they worried that her very young age (she started early and skipped) meant that she had kind of "tapped out." It took us a year for them to grasp she was really gifted. OTOH, her educational psychiatrist was so wowed by her IQ that he really dismissed any other psychiatric concerns.
I don't have a name, but I would also recommend calling one of the teaching hospitals and asking for a neuropsych rec. We get care for another dd (but rheumatology, so that wouldn't help) at Children's in Lincoln Park and we LOVE it - they are by far the best doctors we've seen.
If you got the CTD short eval, we had that done for my youngest in K. It was nice to get some validation but honestly, it didn't tell us anything new. Our dd's full evaluation was about 10 pages, both sides, small print, of extensive information. Although I don't think they really captured everything in terms of her psychological issues, it was still extremely helpful. It cost us, but it was worth it.
I think for 2E kids, there is no straight and easy path. Our dd has had ups and downs, teachers who get her and teachers who are clueless. And she's like your dd in that she likes being challenged, hates stupid or pointless stuff, but used to also meltdown when she thought something was too hard (she liked to be the top at everything, without effort... that obviously can't always happen).
For the record, our dd was diagnosed as a teen with bipolar II, generalized anxiety, and executive functioning deficits. Now, though, she is off all meds and doing pretty well - a senior in college majoring in science and on full academic scholarship (with a LOT of help, and a college very close to our house).
For our part, we've stopped trying to diagnose her. That might seem weird given that I've just said "get the diagnosis" but what I mean is continue to get as much information as you can. Continue to try and figure out what makes her tick. Work with teachers. Be open, don't worry about labels!! I had to get past that. Everyone is somewhere on the spectrum, right? She's just a little more off-center than some, and needs a little more support. She'll never be our easy one, but she's managed to find a good fit. So can your dd.
HAHA - now have I made you feel better about YOUR long post?
Anyway, good luck, I'll stop rambling, but you can feel free to email me if you want to chat more.
Theresa