I think you may still get it to work. If I recall correctly it's when you are asked to enter the code, below the boxes where your code would normally go, there's a "Forgot code" option or something to that effect. When you click that, I think you'll be given the option to reset.
Ahhmt! You are the winner! Thanks for that, finally got it all working now after hitting my head against a brick wall the last few weeks trying to change that phone number. Thank you.
I just have same problem, but i found a solution....
On iOS go to Settings > iCloud > Keychain and tap to button to disable iCloud Keychain. (you will be asked to delete or keep passwords on device) i chose delete....
Then enable it again and in pop-up chose Reset iCloud Keychain, on confirmation pop-up chose Reset
In new pop-up Use iPhone Passcode as iCloud Security Code? chose Use Passcode
Enter your passcode (4 digit) and then chose country and your new phone number
I just changed my number on Iphone 4, 7.1.2