I am unaware of the infant class size rule of Kent
The infant class size rule is a national rule, not something specific to Kent. A class in infants (i.e. Reception, Y1 and Y2) cannot have more than 30 children per teacher. With an admission number of 60, the school clearly has two classes per year in infants so any appeal would be heard under infant class size rules. That means you can only win if you can show that:
- the admission arrangements were contrary to the admissions code or relevant law and this cost your child a place, or
- the admission arrangements were not administered correctly and this cost your child a place, or
- the decision to refuse to admit your child was unreasonable
As you are a late applicant it is extremely unlikely that either of the first two points will apply so the only way to win an appeal would be to show that the decision was unreasonable. The bar for that is very high - in essence the decision must be irrational. Your best chance of success would be if the school offered by the local authority is more than 45 minutes journey each way.
Yes, your son will be one of the oldest in his class. However, he does not have to start full time education until the start of term following his fifth birthday. You could, therefore, defer entry until after Christmas. As Imchlibob says, this involves getting the local authority to offer you a place (which they must do) and then, if it isn't a school you want, telling the school that your son won't be starting school until the New Year.
Holding a deferred place just means you know what your backup plan is while you homeschool, but your child would stay with their age cohort so if starting a year later than normal they would be in the same class but having missed out the first year
I'm afraid this is wrong. You cannot defer beyond the start of term following your child's fifth birthday. After that the place will be allocated to the first child on the waiting list, so your backup plan would be gone. If nothing comes up before Christmas you will have a choice of taking up whatever place the local authority has offered or losing that place, homeschooling and hoping that something better will turn up. Note also that you will not need to homeschool your son if you defer until the New Year as he is not required to be in full-time education until then.