It sounds like she doesn't have as much social anxiety as my daughter - that makes things a little easier
It also sounds like she's advanced everywhere, although which areas are "gifted" as opposed to just advanced can be harder to tell. I think, though, for a kid to be considered gifted, they don't have to score in the gifted range globally. For instance, if she's just extremely bright in math but gifted for reading, she's still gifted (as far as I know, anyway).
So the question is, how high will she test (i.e. high enough to get her into the gifted program)? I got my daughter in without a test, but I had to provide a lot of evidence (which it sounds like you have as well).
Have they told you she cannot get into the program if her test scores are below the gifted range? Look at it this way, if she has a bad day (i.e. distracted, being a kid) and her test scores are below gifted, the school doesn't have to see the results.
Bottom line, you know her best and what she's capable of.
Best of luck
