On the maladministration question, this is pure speculation but I wonder if the panel made the same mistake as I've seen made by some other appeal panels.
Far too regularly I assist with appeals where the parents have applied to their home LA for a place in a school at a neighbouring LA but they've missed out because their home LA failed to pass on the application. More rarely I deal with cases where the home LA has failed to pass an application on to a VA school or academy within the LA. The number of such cases I've dealt with is well into double figures. The parents have won every single case to date but quite a few of them have had to go to the LGO to get it sorted. Some appeal panels have looked simply at the question of whether or not there was a mistake by the admission authority (i.e. the school for a VA school or academy, the school's LA for other schools), decided there wasn't and therefore upheld the decision to refuse admission without looking any wider. The LGO has always been clear in such cases that the appeal panel must look at the whole process when deciding if the child has been deprived of a place in error and has therefore upheld those appeals that have been rejected by appeal panels.
So, looking at this case, it may be that the appeal panel decided that the school got it right but the mistake was made by one of the two LAs and therefore, in their view, didn't count. That is, however, speculation. Without seeing the clerk's notes it is impossible to be sure. But if that was the basis of their decision they were clearly wrong.
Perma - To give you some advice (which is, after all, the point!)...
When a case is referred to the LGO (I know this one is going to the EFA but read on) the normal outcome if they find that there were problems with the appeal is that they recommend a fresh hearing with a different panel. They will only normally recommend that the child is admitted without a further hearing if they conclude that there is only one possible outcome from a correctly conducted appeal.
We don't have much history to go on with the EFA so it is difficult to judge what they will do, but I know there have been a lot of discussions between the EFA and the LGO in an attempt to ensure that they work to common standards. I would therefore approach this the same way I would approach the LGO. I would write to the EFA (or write again if you have already done so!) setting out the sequence of events and pointing out any issues with the way the hearing was conducted and the obvious problems with the decision. I would then quote LGO case 99C01876 and state that the decision in this case has always been understood to mean that an offer made in error cannot be withdrawn more than 3 days after it was made and that therefore a correctly conducted appeal should result in the place being reinstated. I would ask the EFA in light of this to recommend that your daughter is admitted without the need for a further appeal.