Oh dear, oh dear.
I can understand that you must be absolutely fuming and utterly distraught.
First things first, please could you send me a PM with:
a) your postcode and
b) the list of all your preferred schools (not just GS) in the order you put them on the CAF.
I may then be able to reassure you about what might happen to the waiting lists over the next few weeks and months.
An EP report is pretty unlikely to help with a transfer appeal, so before you spend a lot of money unnecessarily let's see what Aunty Sally-Anne's crystal ball reveals.