The extra information is helpful.
It's helpful to you that this is not an infant class size case, because you will be arguing about the relative prejudice (disadvantage) to your child in not being admitted versus the prejudice to the school in admitting another pupil.
Firstly: I'm slightly puzzled by the timing here - did you apply through the usual admissions round or did you apply in-year? If the latter, the Fair Admissions Protocol should apply. The latest version of the admissions appeal code (which you should read) says
Expressing a preference and Fair Access Protocol
3.23 Paragraph 3.9 of the School Admissions Code requires each local authority to have a Fair Access Protocol to ensure that, outside the normal admissions round, a place at a suitable school is secured quickly for unplaced children, especially the most vulnerable. It also requires local authorities to ensure that no school is required to take a disproportionate number of children with challenging behaviour. In circumstances set out in its local authority?s Fair Access Protocol, an admission authority may refuse to admit a child outside the normal admissions round even though places are available (see paragraph 3.12 of the School Admissions Code).
3.24 The allocation of a place in accordance with a Fair Access Protocol does not override a parent?s right to appeal against refusal of a place at any school for which they have applied. If an application has been refused despite there being places available, the governing body must present their case for refusal, demonstrating how admission of the child would prejudice the provision of efficient education or efficient use of resources. When considering such an appeal, in addition to considering the appellant?s arguments for their child to be admitted, the panel must take account of the requirements set out in the local authority?s Fair Access Protocol. The panel must carefully consider whether the presenting officer has clearly proven that admission of the child would be prejudicial to the school or other children.
Looking at the detail: I'm assuming that all the classes in KS2 are combined in some way to make 30+ in each class. Is that right, or are there classes of 30 in Ys 4&5 and 1 1/2 classes in Y6? And you have information to show that one year is already 1 above PAN? You can certainly include that in your arguments, although the LEA will argue that having spaces in some year groups doesn't make it any easier to accommodate your child in a year group that is full, so whether/how the year groups are combined could be important here.
You need to highlight all the reasons why your child would benefit from attending the school - the fact that you have moved to the area and so the school will help your child settle, a sibling already has a place etc etc. You also need to check what the school's admissions criteria say about siblings. Some schools give priority only to younger siblings, but if the preferred school also gives preference to older siblings this may at least help to get your child into a higher priority group on the waiting list.
The issue around your child being on SA+ is complicated. If your child has a disability, the school cannot discriminate against them because of it, but (equally) the Fair Access Protocol says that schools shouldn't be required to take a disproportionate number of pupils with challenging behaviour. A lot could depend here on the reasons why your child is on SA+. Having 15/60 children at SA+ sounds to me (without going to check my LEA's average) on the high side of average, but not unheard of. Your best approach is probably to try to identify enough strong reasons for your child to be admitted that you can convince the panel that they outweigh the disadvantage to the school, including any disadvantage in meeting the needs of another child at SA+.
Lastly, has your child got a place at another school?