Called Barclays today and requested that my Rewards MC (11 months old) be closed and have the CL transferred to my Ring (2 months old) account. The lady was SUPER friendly and helpful and after verifying some info and checking the status of my accounts was able to do it. Was on the phone for a total of 5 minutes. Painless.
This was from calling the backdoor number as when I called the regular number they told me it could not be done. Just as a heads up for those who may have tried and failed. You can call their credit department directly (1-866-408-4064).