The first question is whether or not this will be an infant class size appeal. That depends on the size of classes in Reception, Y1 and Y2. If it is an infant class size appeal you can only win if you can show that a mistake has beenmade. If it is not infant class size you will have a better chance of winning by showing the panel why your child needs to attend this school. Your case must be about your child's needs. Problems you may have with transport, child care, etc. will not help you to win your appeal.
Having said that, I note that Cheshire West and Chester treat a change of address after the deadline for applications as an on time application from your old address. They allow you to change your preferences but still process your application using your old address, which seems singularly obtuse to me. There is a similar case in another thread where a child has been allocated a school 15 miles away near their old address. That case involves another LA but you may want to look at the thread "Appeals, am I reading this wrong?"
You have actually been disadvantaged because you applied on time. If you had applied late you probably wouldn't have got a place at any of your preferred schools but the LA would have dealt with your application using your new address, so you would probably have been allocated a place near your current home. Because you applied on time they have insisted on using your old address so you have a place at a school which is miles away. I would argue that this is perverse. You can win any appeal, including an infant class size case, if you can show that the LA has acted perversely and a reasonable LA would have admitted your son.
In theory, even if an appeal panel accept this argument you should only get a place at the school you would have been allocated if the LA had used your current address, but a sympathetic panel may be prepared to stick their necks out for you.