Not sure if you're in LA or somewhere else on the Gulf Coast, but this is what LA has to say about it - see "Backgrounder - About the Gifted Program," second link in the list:
https://www.louisianabelieves.com/resources/library/academicsLooking at Section 3 - Criteria for Eligibility shows that a K student has a significantly higher threshold than a 1st-grader. The standard matrix they're referring to is a little bit below. If the teachers are on board enough that they're willing to make an official recommendation, then your DD would only need 6 points on the matrix, instead of 10.
My DD's school suggested we wait for full evaluation until after her 6th birthday, at which point she would be measured at the 1st-grade threshold (we took that advice, thinking she wouldn't hit +2.5SD on the RIAS... shows what I know). If your child takes the test and doesn't make the cut, they won't let her take it again for another full year.
Distractability might explain your DD failing to deliver her best results in February, but you said they've screened her twice. That would have been in Pre-K? Not sure how that's even valid.
