Videos are a compilation of many elements, some of which are tied directly to the account under which they were created. As such, moving videos between accounts can't be done without also "breaking" those ties, which also "breaks" the videos. This is why videos on GoAnimate aren't transferrable from one account to another.
The simplest workaround for this scenario is to first change the email address on the free account to the desired email address before you pay for the subscription. You'll have to reach out to email@example.com to process this change. Once this is completed you can login and register for your paid subscription.
If you have already purchased a subscription under a new email address, reach out via firstname.lastname@example.org.