Part 4 should be blank on the proposed statement and the LA should have asked you what your preferred school is.
This is what the Education Act 1996 says about your rights in requesting a school:
'Parents may express a preference for the maintained school ( but not a PRU or
hospital special school) they wish their child to attend, or make representations
for a placement in any other school. LEAs must comply with a parental preference unless the school is unsuitable to the child?s age, ability, aptitude or
special educational needs, or the placement would be incompatible with the efficient education of the other children with whom the child would be educated, or with the efficient use of resources. LEAs must consider parental representations and arrange any meeting(s) with LEA advisers or officers the parents seek, before issuing the final statement.'
If the school is full, the LA may say that a placement would be incompatible with the efficient education of the other children due to overcrowding. However, if you can argue that a mainstream school is inappropriate for your child's SEN, they would have to find a place for you at the maintained special school (or at another special school out of county/independent).
You can make a request for one of the special schools now and the LA will name a placement in the final statement. If you are not happy with the named placement, you can appeal to SEND tribunal, although it takes 4-5 months to get a hearing so it wouldn't be done in time for September. The Tribunal can direct a school to take a child whether there are places or not.
If you are clear about your rights and the LA realises that you will kick up a fuss if they don't name your preference, they may well find there is space for your child after all, without having to go to tribunal.