There currently isn't a builtin way to switch templates by a few clicks of a button.
If you have a paid subscription and wish to move it to your new site, reach out to your account manager and they will be able submit the manual change for you. Keep in mind that it can take up to two weeks for manual subscriptions changes to complete.
Reach out to email@example.com if you have more questions. If you are a Concierge member, give us a call at (888) 534-2183.