I wish you luck!
My dd just started yr 5. She set the top score in her year group for the optional SAT reading test in yr 4 at her "outstanding" primary. I have little expectation that they will consider sitting her for level 6 reading next year or teach her to that level. Of course, I wish they would, but I'd bet the mortgage that they won't even consider it.
Why do I think this? At our "outstanding" school, no one has ever taken the level 6 Reading test. Nationally very few children pass this test. (Statistically, I think it rounds down to 0%.) Our school does no setting/streaming, whatever you want to call it, in literacy, so teaching level 6 to a few kids and teaching level 3 to a few others with the whole range in between in a class of 30 is probably not realistic, despite all the guff about differentiation. Finally, I've read the school news letter with articles written by one of the most respected year 6 teachers, and was shocked by the quality of the writing. My husband initially thought one of the children had made a good effort writing it. Er, no that was written by the teacher! 
In our case, the school could never be "encouraged" into it. I could be very aggressive and demanding, and I might force them into it, but I think it would do more harm than good. The upset, defensive position I would cause, and frustration just wouldn't be worth it.
The only way I can imagine our school coming round to the idea, is from pressure coming from above to sit more children for level 6s. In that case they would suddenly be keen to scoop up my dd and a few others and push them forward. For us the best thing is to just keep providing her with books she likes to read and trying to ask "dinner table questions" that get her thinking.
I realise this isn't an answer to your question. I just wanted to empathise, since I cannot offer more.