Transfering file and folder permissions to a clean install with rsync?
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.

Delete oxprox_2 account or copy into oxprox_3
Create the account to match the restore path
Let the system fix permissions on the restored files
Log in to the new account and test

Basically, delay making the account until after you’ve done the restore.