From the look of it, you received a very thorough evaluation, responding to the outside eval's Dx of autism. That they did not repeat your outside eval categories suggests that they are accepting those findings. You got the ADOS, which, up until the release of the 2nd edition this year (so it's not inappropriate to use the 1st edition), was the gold standard for autism diagnosis, and it appears that it was properly conducted as an arena eval. The other instruments are similarly appropriate (all things I would choose as go-to assessments).
BASC-2:
2,3,4,5,8,9 are all very consistent with the ASD. 1 (& the associated 6, which is actually a composite score comprised of 1 and two other scales) could be consistent with ASD, especially if it is more sensory-seeking behaviors, as hypothesized during the ADOS. 7 would not be that surprising, given the observations of ineffective attempts at engaging with others.
CELF-5:
this is a rating scale as well, completed by one of the same raters as for the BASC-2, BRIEF, and SRS-2, so it's not that surprising that the ratings are similar, just in more detail.
SRS-2:
Note that, in school, the ratings are progressively better as the putative educational fit improves, reaching normal limits in the GT classroom. This may suggest that her social communication performance is better with those who are more skilled at meeting her where she is (better communication partners), most likely, both in the cognitive/academic sense, and because high cognitive partners are better able to adapt to her.
I often see more problematic numbers at home, probably because there is a much wider range of expected responses in the home and community environment, than in the school setting. The rules of school are highly consistent year after year, and even those who are challenged by adapting to fluid social situations can usually figure out enough, and have enough stability in the setting expectations, to manage school. The community, on the other hand, changes all the time. Even the most routinized home also doesn't run on bells and daily agendas. And, of course, many children work really hard at meeting expectations at school, and then let it all out at home.
That she can perform better in some settings suggests that, like many high-cognitive individuals with social communication deficits, she has cognitive understanding of some rules for social engagement, but not automaticity, so she can employ them when supported and highly-motivated, but is probably drained by the effort. (Not unlike the deteriorating spelling and handwriting we've discussed elsewhere, with respect to dysgraphics.)
I'll try to address recommendations a little later in the weekend.
