Hi much more expensive is it pa than the school the LA has chosen? An EHCP placement will be at least £10k pa in a mainstream, and likely more like £13k.
Assuming you want the LA to pay the majority....
If there is less than £4 to £5k difference, ask for your school to be named as parental preference. This means the LA aren't responsible for travel, but they duck out of 6th form travel funding any Way.
Given the scholarship, ask if the school will honour this if the LA pays, which should reduce the difference further. They may not and do not have to, in fact, without asking I'm sure it's unusual.
You can then pay on top for any extras not listed in the EHCP. So if you wanted a private 1 to 1 support lesson you can pay, rather than the LA unless EHCP requires it.
If the EHCP requires a TA, you may need to try to get this reworded to be TA in classes over 15, say, which would mean it wasn't likely needed in the independent but would be in the mainstream. However, things like that usually need an EP to state it as a need and you should take care to sort your child's needs out before the school rather than trying to sort the school first.
Unfortunately you may well have to appeal and you'll be lucky to get a tribunal date before September now.
Assuming you can afford fees. You can ask for a personal budget or for the school of your choice to be paid for additional SEN fees (usually this is limited to the full cost of the maintained school less £10k, ie the top up fee the LA would have otherwise paid). Do this before sending your child, making it clear that this, for the LA, is a cheaper option than paying for the mainstream. Ideally you need agreememt before moving schools.