I do think you need to move up the chain now if the teacher's not helping. The gifted teacher may not be the right person, if they are pushing back about ID-ing. I first went to the class teacher, then the kindergarten gifted teacher. The gifted teacher told me she's not the right person because she just does a one hour pullout once a week, and it is very purposefully not a curriculum or accelerated. It's simply problem solving/comprehension type of exercises to enrich the classroom curriculum.
I was looking for differentiation within the class for worksheet type of work, and someone to teach or design a curriculum that I would teach and have it tied into what the class was doing.
In our school it was the principal I needed to talk to, and she organised everyone for testing and for differentiation. She had the authority to ask the math specialist (who technically is supposed to work with students who are behind) to do the testing, and she is now getting a lesson once a week with the math specialist and her teacher will be given classroom materials. There's also a way for us all to communicate, including work she does at home. I don't know yet how accelerative it will be, hopefully the teacher will be responsive to the pace my DD works at.
I would read up on the different options, like class acceleration, whole grade acceleration, enrichment, differentiation, etc.
Sorry if I get some details wrong or have missed things, I am trying to help, but it's really really hard for me to read the walls of text. Would you mind putting some paragraph breaks in, maybe?
