Your medicals won't just expire, London will see this and either extend them or request you redo them (your application won't be rejected because they have expired whilst its in process)
I do remember reading a case on here where someone had only 1 week to land!! Its rare but can happen, there is no minimum time they have to give you
My suggestion would be, in December order you GCMS notes... this will tell you at what stage your application is.. whether security/ background checks have been started or not, this will give you a better idea if your application is nearing completion or not
Either way your medicals will be the issue here, just hope that London will extend your medicals for you and you can go to NZ and not have to worry
But yes as far as i'm aware threes nothing you can do right now, your just going to have to wait and see how fast/slow your application goes
Its always best to do the things that expire e.g medicals and police checks last.. that way you wont run the risk of them expiring whilst your application is still in process