you could move as planned and then reapply. The council have to find you schooling.
Alternatively, you could home educate whilst putting your son's name on the waiting list/appeal list. or you could home educate for this term and reapply after Christmas. Sometimes at a non intake time of year, you are successful. Alternatively again, you could home educate for this year and reapply in a non intake year.
Good luck with what ever you decide, but if you are about to sign documents, then really it is the coucil's responsibility to find you a place
much love to you and I hope it sorts itself soon.