1. Download the contacts first via outlook if you have your windows live id configured there. 2. Hard reset the phone and sign in with your outlook.com address. Windows phone does not allow switching ID's once you have set it up without hard resetting the device.
Edit - Can you take a screenshot of that 'change your email address warning' and post it here that you see when try and change you email from gmail to outlook.com.
do the email address change that you are being offered above. but what you will need to do is, reset your windows phone afterwards and sign in with your new outlook address that you will enter in the 'change email address' field. it will automatically transfer all the purchases and backend settings to your new outlook.com email address that you will enter when swapping email addresses.