My immediate thoughts:
As we've discussed previously, the fact that the capacity and admission number were set before the recent extension is definitely worth raising. That suggests that the current capacity and admission number are not a fair reflection of the school.
I agree that adding your son will not require an extra class so I don't think the lack of an extra teaching space for one is an issue. If it were me I would probably ask the LA's representative a pointed question about this.
One more child is not going to make the hall significantly more cramped than it already is and in any case, as you say, they are going to have an extra year group next year.
They are obviously trying to make the case that a mixed key stage class (presumably Y2/Y3) is more demanding than a mixed year class within a key stage. I would push them on that one and see if they can justify it, especially given that some schools have mixed key stage classes of up to 30 children.
Regarding your point 5, what they are really saying is that there is no room for another year group unless they relocate the pre-school. They are clearly trying to suggest that the school will be overcrowded next year and therefore adding your son will make it worse.
I've no idea what the situation is nationally but I can't think of any primary schools in my area with a dedicated food tech room.
As you say, the classroom changes are going ahead regardless of whether or not your son is admitted. Make sure the panel understands that.
As Admission says, this looks like a fairly standard statement. I think the stuff we've talked about previously will weaken their case. As they are bringing up the change next year you are clearly going to have to talk about that, though. There are no guarantees - it all depends on what the panel you get thinks of it. But I don't see anything here that suggests a change of tack is needed.