Are you appealing B&F as well as I? You should. If B&F don’t accurately reflect DD’s needs and the provision she reasonably requires, which you are saying they don't, any consultation is going to be inaccurate and section I is the logical conclusion of B&F so the placement named may also be inappropriate.
What other evidence you need depends on what you already have.
Is the school wholly independent? It doesn’t sound like it. If it isn’t, you don’t need an offer of a place or for the school to agree. The law says your preferred placement must be named unless the LA can prove:
-The setting is unsuitable for the age, ability, aptitude or special educational needs (“SEN”) of the child or young person; or
-The attendance of the child or young person would be incompatible with the provision of efficient education for others; or
-The attendance of the child or young person would be incompatible with the efficient use of resources.
The bar to be able to prove one of these is higher than many LAs admit.
To show these don’t apply, think about seeking independent Ed Psych, SALT and OT assessments. However, as this is a phase transfer appeal, when is your hearing? You may have left it too late unless you are very lucky and get a cancellation.
If you think DD doesn't require the things they are saying she does, do you have evidence from the current school DD doesn't require them?
You should ask exactly what the incompatibility is. Staffing can be written into F, so that on its own wouldn’t make placement incompatible. The LA must ensure the provision in F is provided, that includes funding it an at appropriate level.
Having said all that, are you sure DD will cope in a mainstream secondary? Are you sure she doesn’t require the support stated in the EHCP?