You can't change one type of object to another, other than by recreating it and copying the values. The latter is not possible for users because you can't read the password.
So there are 2 options.
You could either give these people a new account with a new password, but you'd have to go through some trouble if there are references to the user entity from other entities.
Or you could just keep using system.user. There's no real problem with that either other than some convenience stuff in the account entity such as for changing passwords. It has worked for this application so far. You may have to recreate some of the administration forms though.
In new applications you would probably have system.user -> administration.account -> your own object.
Because of the upgrade you now probably have system.user->administration.account and system.user->your own object.
But would it not be possible to let administration.account inherrit from your own object instead of system.user? This way you can make sure every object gets an administration.account without breaking al the references.