Welcome!
Short answer, part 1: no, there is not a meaningful difference between 129 and 130.
Long answer, part 1: As a parent, I get your frustration--but as someone who has been on the other side of the table for GT decision-making, I also understand why the district has to have policies. If there were none, those children with more savvy parental advocates and the financial resources to obtain private testing would gain an advantage over children with identical profiles without those resources. And since the children without built-in advocates tend to be disadvantaged to begin with (they usually have to overcome more to achieve the same nominal qualifications), this creates equity issues. Not to mention lawsuits and OCR investigations.
Short answer, part 2: yes.

Long answer, part 2: SAGES-2 contains two types of tasks. The aptitude measure is essentially a nonverbal cognitive (IQ) screener, which is not as robust as the WISC-V, since it is a screener, but does have the advantage over InView that it is individually-administered, which allows the examiner to gauge and maintain student attentiveness and engagement. The achievement measure consists of a language-related task (verbal and social studies), and a math-related task (math and science). By my recollection, US state capitols do not have a prominent place in scoring.
In the case of your DC, the SAGES-2 aptitude measure may or may not increase her likelihood of GT qualification, as it principally assesses her apparent weakest area on the InView. However, on the WISC-V, the task is most similar to the FRI, which was a strength. Perhaps the difference is related to group vs individual assessment, in which case the result may be more like that on the WISC, but that is difficult to predict from the available data. The achievement measure, OTOH, may have a more clearly positive effect, since you describe her as an early and avid reader, which typically has score-raising effects not only on language/knowledge-related tasks, but on science-knowledge-related tasks.
Scoring on the SAGES-2 can be reported using either population norms (in which case the district is probably looking for a number at or above the 98th %ile), or GT norms, in which case the cutoff is probably more like the 50th %ile (i.e., at or above the mean for identified GT students).