Converting an existing user to a restricted profile
As of this moment, it is not possible to convert a user into a profile. 

However, you could create a profile based on the existing user. Downside: Since a profile doesn't have a Google account tied to it, they can't have a GMail app. And as you have already mentioned, they would also lose those user-specific data.

UPDATE #1: From Android.com, it says that a restricted profile is a subset of a user's account. It's using the same user account, albeit restricted. So the profile is quite different from a User, where it's tied to a different Google account.


  Each restricted profile offers an isolated and secure space with its
  own local storage, home screens, widgets, and settings. Unlike with
  users, profiles are created from the tablet owner’s environment, based
  on the owner’s installed apps and system accounts. The owner controls
  which installed apps are enabled in the new profile, and access to the
  owner’s accounts is disabled by default.