Mmm...I think you need to first of all think really carefully about what your DD needs, and THEN how to achieve what she needs.
I think there is overall a tendency to think that more support (ie. 1:1)= better support. However, if the 'vehicle for delivery' of support is wrong, then adjusting the amount of it is going to do nothing for the child. A bit like getting a bigger boat when the destination is reached by car, or upgrading to a people mover when the destination is on water.
The SEN CoP doesn't say 'more support' or even '1:1 support'. It says:
"Special educational provision means:
(a) for children of two or over, educational provision which is additional to,
or otherwise different from, the educational provision made generally for
children of their age in schools maintained by the LEA, other than special
schools, in the area" SEN Code of Practice Pg 6
So, as parents, its important that we don't argue 'my child has SEN, therefore they need 1:1 support, because the SEN CoP says that SEN= more support', because we are missing half of the information.
An example, in DD1's Special School, is that her school is very well resourced with SALT. We have 3 NHS SALTS who are based at DD's school, and they also consult and give SALT for children in other schools. But, essentially, if you need to speak with a SALT, you can just phone the school.
However, they have changed their practice. They used to give direct SALT 1:1. Then they realised that a) the support they were able to give was not efficient, and not frequent enough. Children with significant SEN need that routine to build on new knowledge. b) the motivation for SALT wasn't very strong, because the SALT wasn't that important to the children. They only saw him/her once per week, say, or even every day for 10 minutes, but then the rest of the time they forgot them.
So, instead, they do 'communication groups' in class. In that group, they model the 'next step' techniques in the group session, and then for the rest of the week/fortnight, the teachers and LSAs use those techniques all day, every day. The SALT has more time to assess and monitor progress, and the teaching staff can pop in to see them if they have any concerns. Additionally, if they feel that there is something specific that a child needs to work on 1:1, they then give 1:1 SALT to that child in addition.
The pivotal point of your argument is pinned on whether the support your DD gets at the moment is a) effective b)sufficient. You have an EP who is saying 'this support is actually hindering your child'. And you are saying 'this support is what my child needs'.
I think, if it were me, I would be trying to find a way that we could meet in the middle, unless I was sure that only that provision would work. I've said before that DD1 needed 1:1 completely at pre-school, and I thought she would at school. Now, she is at special school, and she doesn't get 1:1 support. She is in a class of 10 with 5-6 teaching staff. She copes well. BUT her environment is just right for her. It would actually be cheaper for her LA to give her 1:1 in mainstream school, but it wouldn't meet her needs.
SO, is it 1:1 your DD needs, or is it something else? Or a combination of reduced 1:1 and something else? If you are sure it is just 1:1, then previous posters are right, you can get your way by proposing something reasonable but much more expensive, usually. If you are at all doubtful that 1:1 alone will meet your DD's needs, you need to look around and see what provisions are available.