As you have discovered Time Machine and the system migration scripts handle all the little corners where files are customized per unique account or tied into a system file or just not to be backed up. I would probably rsync back the files into a new short name for which no user exists on the system.
Then take advantage of the system to fix permissions by creating the new user and answering yes when it sees the home folder present matching the short name of the user you are about to create.
Basically, delay making the account until after you’ve done the restore.