I had serious trouble with D23 contacts - because most of it is run through the "Disney Store" online - I hadn't received my renewal info, and it took 3 months to resolve - I hope you have better luck!!!
For any changes that need to be made to membership, you have to go through disneystore.com. If you go to disneystore.com and click "Guest Services" in the top left corner it gives you the option to email them. Be sure to send them your name, membership number, the order number from when you purchased or renewed your membership (can be found by clicking on your account and searching through your past orders), as well as your old address and the address you are moving to.
I changed my address on my membership in January which was quick and painless, but that is the information they will need. If you contact D23's own customer service team, they will refer you to Disney Store since they handle all physical aspects of membership (anything that is mailed to your house that isn't part of an event or the Expo).
I'm attempting to watch and review every Disney movie ever made in my blog called The Disney Films. You can also follow me on Twitter for news on upcoming Disney films.