How do you hand off and rename a custodial NEAR account to a user?

Question

A toy example:

1. The application NFTApp created a new account throwaway.near for a new user and minted some NFTs into it. NFTApp has the only full access key to throwaway.near. The user doesn't even know what a seed phrase is.

2. At a later time, the user decides they want to take possession of this account and its contents but name it keeper.near. Maybe they have created keeper.near previously or maybe they create it fresh as part of this process. Either way, the user controls the only full access key to keeper.near.

3. NFTApp then deletes throwaway.near and recovers the storage tokens from it.

How can we effect this handoff without needing to manually send contents from throwaway.near to keeper.near?