Honestly, I had originally signed her up for the 8th grade Stanford test last July as well, because at that point my main concern was making sure she had adequately mastered her lessons before allowing her to begin high school material. (She tested above average academically on the 8th grade test as well.) I've never normally been worried about comparing her to age peers, just about evaluating academic mastery. However, in terms of intent with "labels", our needs shifted this past autumn, and that was why I had her take an actual 5/6th grade (age-equivalent) Stanford exam, as well as the online SB.
I wasn't going to mention religious activities in my original post. But we are members of a church, and I needed to explain to the pastor this spring why my daughter would not fit well into the "required" religious education classes. (Her philosophy and historical studies have taken her beyond her age peers, and she found the classes underwhelming.) So, normally yes, labels are not an issue when she is only enjoying theater or piano, but certain other activities do have a more rigid structure that require firm argument.
Also, with her beginning high school level material this year, we have begun exploring college roadmaps, and I realized I might need to prepare to advocate in that arena as well. I had thought of something similar to what aeh suggested, reporting her at grade 11 regardless of her age. Currently, based on her abilities and interests, we are considering allowing her to CLEP some subjects when she is 13-14, then take part-time classes to finish off online community college for dual credits when she is 15-16. I do not think I want to throw her into an in-person campus environment too young, echoing your concerns, FrameistElite, but I'm hoping online classes will be fine.
As you suggested, she does however have some weaknesses, specifically in her study and executive skills that I mentioned in another post. I've encouraged her to be fully flexible if we need to slow down and take more than one year on a subject, but even if we pulled her back a year, she would still be ahead enough to need a game plan.
