To deal with the obvious first.
This was not a class size case.
The PAN is NOT 245. The PAN is the admission number, i.e. the number of children that will be admitted to Reception each year. If they admit 245 to Reception every year the school will be very full - over 1700 children! The figures you have given suggest that the PAN is actually 35, meaning that there would be 245 children in the school if every year was full. If they have 35 children in the relevant year (Y2 for your son) they are up to PAN. The fact that the school is under the 245 it would have if it admitted up to PAN every year doesn't change that fact.
If your neice was kicked out of a school she was attending for being outside the catchment area that was a serious error. Once you have a place at the school and have started attending it can only be taken away from you if the place has been obtained fraudulently, and even then it can only be taken away during the child's first term at the school. However, if your neice failed to gain a place because she was outside the catchment area there is nothing wrong with that.
There is nothing wrong with families moving out of the area and continuing to attend the school. They are legally entitled to do so. The LA CANNOT take a pupil's place away just because they have moved. The LA will not measure the distance from pupil's new homes when they move, so the LA representative was telling the truth.
Have you had the appeal panel's decision in writing yet? If that states that the prejudice to the school from admitting your son outweighed the prejudice to your son then the panel have dealt with the case correctly.
As Admission says, you cannot go to the LGO and argue that the panel made the wrong decision. The only basis for going to the LGO is that the wrong procedure was followed. A panel member answering questions may be a start towards that depending on what the questions were, but it may not be enough on its own. So far nothing else you have said constitutes a procedural irregularity, I'm afraid.
In addition to thinking about whether you can put together a case for the LGO, you should make sure your children are on the waiting list for this school.