It is a shame you turned down the school offered. If the subject comes up treat it with caution. If the panel feel you are attempting to blackmail them (or the LA) into giving your children places at your preferred school it will not help your case. Should you lose your appeal the LA is not under any obligation to come up with an alternative offer for you. If they do it may be worse than the school you have already rejected.
I would challenge the playground bumps and minor accidents. They happen in all schools. Ask them if they can prove that these accidents were directly attributable to overcrowding. I would be surprised if they can.
Hot, stuffy and packed assembly hall and crowded corridors are fairly standard statements. As they are only 4 over net capacity that shouldn't really be an issue. Again, ask if there have been any incidents directly attributable to overcrowding.
Only enough tables and space for 30 children can't be right. On the numbers you have quoted they must be running some classes with 31 pupils. Challenge that.
Ask the LA tomorrow to provide the calculated capacity for the school urgently - you need to see that before the appeal. That will be a range and the net capacity will be somewhere within that range. If they have set the net capacity right at the top of the calculated range you should ignore it as it doesn't help you. However, if the higher figure for the calculated capacity is 366 or more you can point out that this suggests the school can take your children without serious problems.
If you want to talk about your son's sporting ability and your daughter's musical activities make sure you take evidence to support their ability/current activities.
Note that the panel will consider the two cases separately. You may find that they award a place for one of your children but not the other. In order to reduce the chances of that happening you may want to talk about the need for them to be together to support each other given that you are moving so far.