I moved my seat this summer. I had to renew first before calling the ticket office during the relocation window. In truth I found it a ball-ache. A twenty minute call (I had to give up to carry on working) was followed by a lunchtime call. I was cut off at exactly 1pm (their lunchtime). I ended up getting through on the tea-time after about 45 minutes on hold.
I have previously moved mid-season also, but that was about twenty years ago so I can't remember how that went, and the experience is likely irrelevent now anyway.
Good luck.