If this is an appeal for the normal point of entry (and it sounds as if it is from "The LA website states that appeals will be held between April and July")
, and therefore part of a batch of appeals, then there is no way it can be postponed for several months because decisions on all the other cases would be delayed.
I suggest you contact the LA to ask if you should withdraw your appeal - provided that they will allow you to submit a fresh appeal later on.
NB: normally you can only appeal once
for a particular year group, and you would need to ensure that the LA won't count the withdrawn appeal as your one and only chance!
(However, a change of address could possibly be considered a significant change in circumstances, entitling you to a second appeal. You might want to sound them out about this - it would be entirely at their discretion.)
There are pros and cons with regard to late appeals.http://www.elevenplusexams.co.uk/appeal ... school#c22