It is most definitely a case of the parent that shouts the loudest gets what their child needs.
Lots of us on here have had similar issues. If you are supported by all those people (particularly if the school say that they couldn't meet their needs without her being Statemented, which is the ONLY criteria for a Statement, whatever anyone tells you) then appealing to SENDIST should provoke a swift U-turn by the LEA because of the high chances that your Tribunal application would be successful.
You need to download a copy of the SEN Code of Practice ASAP, and start looking at the IPSEA website (www.ipsea.org). If you can get through on their phone lines, they can be v helpful.
Parent Partnership organisations in some areas can be helpful, but aren't always independent enough from the LEA.
I found that writing to my MP helped me get the right outcome too!
Take heart - J was turned down for assessment at age 3 (saying that school would be able to meet his needs without a statement - school said er no, we won't) - I wrote to my MP and put in the appeal form to SENDIST and the LEA backed down and agreed to assess, giving him 75% 1:1 TA support. When we wanted that upped to full time, we again had to write to MP and fill in an appeal form before the LEA agreed to do what was right and, significantly, what had been recommended by professionals and parents. He now has full-time 1:1, and some OT, SALT and behavioural support .
It takes time and it takes determination in many cases because the gits are so so reluctant to spend money . Saying no to virtually everyone works as a virtual screening system, like saying that only those who really want it will fight for it.
So sorry that you have to go through this, as I know how hard it is, but you WILL get there. Just remember that you have to prove them wrong and use everything that you can to do that.
Good luck.