how to change iCloud account on iPhone, without deleting data on iPhone

I recently changed the email address associated with my Apple ID. In my iPhone, I have iCloud set to back up my phone's documents and data, but it has stopped working because it's still set up with my old email address. I read that in order to change it to my new email address, I have to delete the old iCloud account (under iPhone settings) and sign in with my new email address. However, when I press 'delete account' it gives me the warning: "If you delete your account, all documents stored in iCloud will be deleted from this iPhone." This is something I do NOT want, as there are documents and app data on my phone that I don't want to lose. (Some people on the forums were saying it gave them the option to keep all their data on their phone after they pressed delete. Mine did not--it only gave me the warning and a chance to cancel, so I assume Apple changed it between now and late last year when those comments were posted.)

So...

- First off, why would they make it this way??

- And more importlantly, how can I get around this? I just want iCloud to back up my iPhone using my new email address, without erasing data from my phone.

Thanks!

Joe